Transformations: Rotations on a Coordinate Plane Meet TED. TED is going to help us learn about rotations.
|
|
|
- Herbert Lawrence
- 9 years ago
- Views:
Transcription
1 Meet TED. TED is going to help us learn about rotations. First let s focus on TED s eyes. What are the coordinates of his left eye? What are the coordinates of his right eye? Good, now you will need to use those coordinates in order to help you discover to rules for rotations. Before we go any further lets discuss the direction in which we rotate. Remember that our coordinate plane is broken into quadrants numbers 1 4. When we rotate we always go in order of quadrant unless told otherwise. II y I A full rotation is 360 so if you rotate halfway around that would be a rotation. A 90 rotation moves of the way around, which just means it moves one quadrant counter-clockwise. If you rotated a figure 90 from quadrant 4 it would then be in quadrant. Let s start with the easy one. What happens when TED rotates 180? III IV x What are the new coordinates of TED s left eye? (, ) What are the new coordinated of TED s right eye? (, ) Write a rule for a 180 rotation. (x, y) (, )
2 Now let s see what happens when we only rotate him 90. What are the new coordinates of TED s left eye? (, ) What are the new coordinated of TED s right eye? (, ) Write a rule for a 90 rotation. (x,y) (, ) A 270 is like doing a 90 rotation 3 times. This means we will go of the way around. What are the new coordinates of TED s left eye? (, ) What are the new coordinated of TED s right eye? (, ) Write a rule for a 270 rotation. (x,y) (, )
3 Independent Practice Directions: Tell where each point would end up if it rotated the given distance. Given Point 90 rotation 180 rotation 270 rotation ex (1, 7) (-7,1) (-1, -7) (7, -1) 1. (2, 9) 2. (3, -5) 3. (-8, 2) 4. (-5, -8) 5. (4, 4) 6. (3, 0) Directions: Rotate each figure the given distance. Sketch the new shape and label the points. Rotate the figure 180 Rotate the figure 90 Rotate the figure 270 Rotate the figure 180
4 Answer KEY Meet TED. TED is going to help us learn about rotations. First let s focus on TED s eyes. What are the coordinates of his left eye? (6, 5) Be careful here, a lot of students (as well as me the first time) mix up TED s left eye with their own left. What are the coordinates of his right eye? (4, 5) Good, now you will need to use those coordinates in order to help you discover to rules for rotations. Before we go any further lets discuss the direction in which we rotate. Remember that our coordinate plane is broken into quadrants numbers 1 4. When we rotate we always go in order of quadrant unless told otherwise. II y I A full rotation is 360 so if you rotate halfway around that would be a 180 rotation. A 90 rotation moves of the way around, which just means it moves one quadrant counter-clockwise. If you rotated a figure 90 from quadrant 4 it would then be in quadrant I. Let s start with the easy one. What happens when TED rotates 180? III IV x What are the new coordinates of TED s left eye? (-6,-5) What are the new coordinated of TED s right eye? (-4, -5) x and y changed to their opposites Write a rule for a 180 rotation. (x, y) (-x, -y)
5 Now let s see what happens when we only rotate him 90. What are the new coordinates of TED s left eye? (-5, 6) What are the new coordinated of TED s right eye? (-5, 4) y became x and changed to its opposite x became y Write a rule for a 90 rotation. (x, y) (-y, x) A 270 is like doing a 90 rotation 3 times. This means we will go of the way around. What are the new coordinates of TED s left eye? (5, -6) What are the new coordinated of TED s right eye? (5, -4) x became y and changed to its opposite y became x Write a rule for a 270 rotation. (x,y) (y, -x)
6 Independent Practice Directions: Tell where each point would end up if it rotated the given distance. Given Point 90 rotation 180 rotation 270 rotation ex (1, 7) (-7,1) (-1, -7) (7, -1) 1. (2, 9) (-9, 1) (-2, -9) (9, -2) 2. (3, -5) (5, 3) (-3, 5) (-5, -3) 3. (-8, 2) (-2, -8) (8, -2) (2, 8) 4. (-5, -8) (8, -5) (5, 8) (-8, 5) 5. (4, 4) (-4, 4) (-4, -4) (4, -4) 6. (3, 0) (0, 3) (-3, 0) (0, -3) Directions: Rotate each figure the given distance. Sketch the new shape and label the points. Rotate the figure 180 Rotate the figure 90 Rotate the figure 270 Rotate the figure 180 Looks the same only the corners would move.
Three daily lessons. Year 5
Unit 6 Perimeter, co-ordinates Three daily lessons Year 4 Autumn term Unit Objectives Year 4 Measure and calculate the perimeter of rectangles and other Page 96 simple shapes using standard units. Suggest
Questions: Does it always take the same amount of force to lift a load? Where should you press to lift a load with the least amount of force?
Lifting A Load 1 NAME LIFTING A LOAD Questions: Does it always take the same amount of force to lift a load? Where should you press to lift a load with the least amount of force? Background Information:
Grade 7/8 Math Circles November 3/4, 2015. M.C. Escher and Tessellations
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Tiling the Plane Grade 7/8 Math Circles November 3/4, 2015 M.C. Escher and Tessellations Do the following
ANALYSING THE SHORT STORY CONTENTS
English: The Short story. 1.x/ fall 2002/lm 1/5 ANALYSING THE SHORT STORY CONTENTS THE SHORT STORY GENRE CONVENTIONS: 2 In medias res beginning: 2 A limited number of characters. 2 Limited character description:
Lesson 29: Lenses. Double Concave. Double Convex. Planoconcave. Planoconvex. Convex meniscus. Concave meniscus
Lesson 29: Lenses Remembering the basics of mirrors puts you half ways towards fully understanding lenses as well. The same sort of rules apply, just with a few modifications. Keep in mind that for an
Subject: Math Grade Level: 5 Topic: The Metric System Time Allotment: 45 minutes Teaching Date: Day 1
Subject: Math Grade Level: 5 Topic: The Metric System Time Allotment: 45 minutes Teaching Date: Day 1 I. (A) Goal(s): For student to gain conceptual understanding of the metric system and how to convert
Integers (pages 294 298)
A Integers (pages 294 298) An integer is any number from this set of the whole numbers and their opposites: { 3, 2,, 0,, 2, 3, }. Integers that are greater than zero are positive integers. You can write
(Least Squares Investigation)
(Least Squares Investigation) o Open a new sketch. Select Preferences under the Edit menu. Select the Text Tab at the top. Uncheck both boxes under the title Show Labels Automatically o Create two points
MODERN APPLICATIONS OF PYTHAGORAS S THEOREM
UNIT SIX MODERN APPLICATIONS OF PYTHAGORAS S THEOREM Coordinate Systems 124 Distance Formula 127 Midpoint Formula 131 SUMMARY 134 Exercises 135 UNIT SIX: 124 COORDINATE GEOMETRY Geometry, as presented
3.1 Solving Systems Using Tables and Graphs
Algebra 2 Chapter 3 3.1 Solve Systems Using Tables & Graphs 3.1 Solving Systems Using Tables and Graphs A solution to a system of linear equations is an that makes all of the equations. To solve a system
Charts, Tables, and Graphs
Charts, Tables, and Graphs The Mathematics sections of the SAT also include some questions about charts, tables, and graphs. You should know how to (1) read and understand information that is given; (2)
Absolute Value Equations and Inequalities
. Absolute Value Equations and Inequalities. OBJECTIVES 1. Solve an absolute value equation in one variable. Solve an absolute value inequality in one variable NOTE Technically we mean the distance between
Three-Dimensional Figures or Space Figures. Rectangular Prism Cylinder Cone Sphere. Two-Dimensional Figures or Plane Figures
SHAPE NAMES Three-Dimensional Figures or Space Figures Rectangular Prism Cylinder Cone Sphere Two-Dimensional Figures or Plane Figures Square Rectangle Triangle Circle Name each shape. [triangle] [cone]
Inv 1 5. Draw 2 different shapes, each with an area of 15 square units and perimeter of 16 units.
Covering and Surrounding: Homework Examples from ACE Investigation 1: Questions 5, 8, 21 Investigation 2: Questions 6, 7, 11, 27 Investigation 3: Questions 6, 8, 11 Investigation 5: Questions 15, 26 ACE
Determine If An Equation Represents a Function
Question : What is a linear function? The term linear function consists of two parts: linear and function. To understand what these terms mean together, we must first understand what a function is. The
6. LECTURE 6. Objectives
6. LECTURE 6 Objectives I understand how to use vectors to understand displacement. I can find the magnitude of a vector. I can sketch a vector. I can add and subtract vector. I can multiply a vector by
Transformations Worksheet. How many units and in which direction were the x-coordinates of parallelogram ABCD moved? C. D.
Name: ate: 1. Parallelogram ABC was translated to parallelogram A B C. 2. A shape is shown below. Which shows this shape transformed by a flip? A. B. How many units and in which direction were the x-coordinates
Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations
Math Buddies -Grade 4 13-1 Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations Goal: Identify congruent and noncongruent figures Recognize the congruence of plane
9.4. The Scalar Product. Introduction. Prerequisites. Learning Style. Learning Outcomes
The Scalar Product 9.4 Introduction There are two kinds of multiplication involving vectors. The first is known as the scalar product or dot product. This is so-called because when the scalar product of
Lesson/Unit Plan Name: Patterns: Foundations of Functions
Grade Level/Course: 4 th and 5 th Lesson/Unit Plan Name: Patterns: Foundations of Functions Rationale/Lesson Abstract: In 4 th grade the students continue a sequence of numbers based on a rule such as
PUSD High Frequency Word List
PUSD High Frequency Word List For Reading and Spelling Grades K-5 High Frequency or instant words are important because: 1. You can t read a sentence or a paragraph without knowing at least the most common.
Geometric Optics Converging Lenses and Mirrors Physics Lab IV
Objective Geometric Optics Converging Lenses and Mirrors Physics Lab IV In this set of lab exercises, the basic properties geometric optics concerning converging lenses and mirrors will be explored. The
ex) What is the component form of the vector shown in the picture above?
Vectors A ector is a directed line segment, which has both a magnitude (length) and direction. A ector can be created using any two points in the plane, the direction of the ector is usually denoted by
Radicals - Multiply and Divide Radicals
8. Radicals - Multiply and Divide Radicals Objective: Multiply and divide radicals using the product and quotient rules of radicals. Multiplying radicals is very simple if the index on all the radicals
CRIME SCENE EVALUATION LAB
FORENSIC SCIENCE INTRODUCTION ACTIVITY #12 NAME DATE HR CRIME SCENE EVALUATION LAB Objective You will draw rough and final sketches of a crime scene. Introduction Once the photographer has completed his
Why is this important to me?
Intro: Before You Quit Your Job 10 Real-Life lessons Every Entrepreneur Should Know About Building a Multimillion Dollar Business Written by Robert Kiyosaki This book can be seen as a road map of skill
Objectives After completing this section, you should be able to:
Chapter 5 Section 1 Lesson Angle Measure Objectives After completing this section, you should be able to: Use the most common conventions to position and measure angles on the plane. Demonstrate an understanding
The Holy Spirit is with you all the time. He is with you when (Mark out all the X s and J s to find out some times the Holy Spirit is with you.
The Holy Spirit Remember what you learned from the Bible verse John 1:12: All people (men, women, girls, boys) who receive Jesus and believe in Him become children of God. I am a of God. A new verse to
4 The Rhumb Line and the Great Circle in Navigation
4 The Rhumb Line and the Great Circle in Navigation 4.1 Details on Great Circles In fig. GN 4.1 two Great Circle/Rhumb Line cases are shown, one in each hemisphere. In each case the shorter distance between
Thin Lenses Drawing Ray Diagrams
Drawing Ray Diagrams Fig. 1a Fig. 1b In this activity we explore how light refracts as it passes through a thin lens. Eyeglasses have been in use since the 13 th century. In 1610 Galileo used two lenses
Johari Window. Lesson Plan
xxx Lesson 12 Johari Window Overview: This optional lesson provides a look into how we view ourselves and how others view us. It is also a model for opening up the lines of communication with others. It
2. Select Point B and rotate it by 15 degrees. A new Point B' appears. 3. Drag each of the three points in turn.
In this activity you will use Sketchpad s Iterate command (on the Transform menu) to produce a spiral design. You ll also learn how to use parameters, and how to create animation action buttons for parameters.
1) The subject. The man walked down the street. 2) A participle (word ending in ing or ed) Walking up the street, he tripped.
1) The subject The man walked down the street. 2) A participle (word ending in ing or ed) Walking up the street, he tripped. Worried about tripping, he bumped into his wife. 3) A connective As she walked,
The Force Table Introduction: Theory:
1 The Force Table Introduction: "The Force Table" is a simple tool for demonstrating Newton s First Law and the vector nature of forces. This tool is based on the principle of equilibrium. An object is
Physics 25 Exam 3 November 3, 2009
1. A long, straight wire carries a current I. If the magnetic field at a distance d from the wire has magnitude B, what would be the the magnitude of the magnetic field at a distance d/3 from the wire,
Section 9.1 Vectors in Two Dimensions
Section 9.1 Vectors in Two Dimensions Geometric Description of Vectors A vector in the plane is a line segment with an assigned direction. We sketch a vector as shown in the first Figure below with an
Lesson 26: Reflection & Mirror Diagrams
Lesson 26: Reflection & Mirror Diagrams The Law of Reflection There is nothing really mysterious about reflection, but some people try to make it more difficult than it really is. All EMR will reflect
Centers of Triangles Learning Task. Unit 3
Centers of Triangles Learning Task Unit 3 Course Mathematics I: Algebra, Geometry, Statistics Overview This task provides a guided discovery and investigation of the points of concurrency in triangles.
TEACHER S GUIDE TO RUSH HOUR
Using Puzzles to Teach Problem Solving TEACHER S GUIDE TO RUSH HOUR Includes Rush Hour 2, 3, 4, Rush Hour Jr., Railroad Rush Hour and Safari Rush Hour BENEFITS Rush Hour is a sliding piece puzzle that
Angles and Quadrants. Angle Relationships and Degree Measurement. Chapter 7: Trigonometry
Chapter 7: Trigonometry Trigonometry is the study of angles and how they can be used as a means of indirect measurement, that is, the measurement of a distance where it is not practical or even possible
Trigonometric Functions and Triangles
Trigonometric Functions and Triangles Dr. Philippe B. Laval Kennesaw STate University August 27, 2010 Abstract This handout defines the trigonometric function of angles and discusses the relationship between
Using VLOOKUP to Combine Data in Microsoft Excel
Using VLOOKUP to Combine Data in Microsoft Excel Microsoft Excel includes a very powerful function that helps users combine data from multiple sources into one table in a spreadsheet. For example, if you
M 1310 4.1 Polynomial Functions 1
M 1310 4.1 Polynomial Functions 1 Polynomial Functions and Their Graphs Definition of a Polynomial Function Let n be a nonnegative integer and let a, a,..., a, a, a n n1 2 1 0, be real numbers, with a
Lesson 17. Introduction to Geometry. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 17 Introduction to Geometry Objectives Understand the definitions of points, lines, rays, line segments Classify angles and certain relationships
Unit 6 Direction and angle
Unit 6 Direction and angle Three daily lessons Year 4 Spring term Unit Objectives Year 4 Recognise positions and directions: e.g. describe and find the Page 108 position of a point on a grid of squares
The GED math test gives you a page of math formulas that
Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding
Lab 37: Magnetic Field ; Magnets - Drawing magnetic fields - Magnetic poles - Forces between magnets
Lab 37: Magnetic Field ; Magnets - Drawing magnetic fields - Magnetic poles - Forces between magnets 1) The following simple magnet configurations were shown to you in class - draw the magnetic field lines
Areas of Polygons. Goal. At-Home Help. 1. A hockey team chose this logo for their uniforms.
-NEM-WBAns-CH // : PM Page Areas of Polygons Estimate and measure the area of polygons.. A hockey team chose this logo for their uniforms. A grid is like an area ruler. Each full square on the grid has
The purposes of this experiment are to test Faraday's Law qualitatively and to test Lenz's Law.
260 17-1 I. THEORY EXPERIMENT 17 QUALITATIVE STUDY OF INDUCED EMF Along the extended central axis of a bar magnet, the magnetic field vector B r, on the side nearer the North pole, points away from this
Topics. Elements of the Law Offside Position Involvement in Active Play. Infringements Recommendations
Law 11 Offside Topics 2 Elements of the Law Offside Position Involvement in Active Play Interfering with an opponent Interfering with play Gaining an advantage Infringements Recommendations Elements of
Drills to Improve Football Skills www.ulster.gaa.ie 1
Drills to Improve Football Skills www.ulster.gaa.ie 1 Drills to Improve Football Skills Drills to Improve Football Skills has been designed with the intention that the coach should step back to take a
Second Grade The Human Body-Cells Assessment
Second Grade The Human Body-Cells Assessment 1a. The basic unit of all life is: a. a tree b. a cell 1b. The basic unit of all life is: a. a tree b. a cell c. an egg d. a phone 1c. The basic unit of all
Styles of leadership. Styles of leadership
Styles of leadership Do you recognise different styles of leadership? Do you use different styles of leadership? Are you accountable for decisions made by your team? In the BS2 session What is leadership?
Introduction. Understanding that God Has a Purpose for Your Life FULFILLING IFE
14 FULFILLING GOD OD S PURPOSE FOR YOUR LIFE IFE (This lesson is designed to teach us that God has a specific purpose for each one of us, and encourage us to discover, pursue and fulfill God s purpose
Accommodated Lesson Plan on Solving Systems of Equations by Elimination for Diego
Accommodated Lesson Plan on Solving Systems of Equations by Elimination for Diego Courtney O Donovan Class: Algebra 1 Day #: 6-7 Grade: 8th Number of Students: 25 Date: May 12-13, 2011 Goal: Students will
Draw pie charts in Excel
This activity shows how to draw pie charts in Excel 2007. Open a new Excel workbook. Enter some data you can use your own data if you wish. This table gives the % of European holidays sold by a travel
Mathematics Second Practice Test 1 Levels 4-6 Calculator not allowed
Mathematics Second Practice Test 1 Levels 4-6 Calculator not allowed Please read this page, but do not open your booklet until your teacher tells you to start. Write your name and the name of your school
Lesson 18: Looking More Carefully at Parallel Lines
Student Outcomes Students learn to construct a line parallel to a given line through a point not on that line using a rotation by 180. They learn how to prove the alternate interior angles theorem using
A Guide to Using Excel in Physics Lab
A Guide to Using Excel in Physics Lab Excel has the potential to be a very useful program that will save you lots of time. Excel is especially useful for making repetitious calculations on large data sets.
Torque and Rotation. Physics
Torque and Rotation Physics Torque Force is the action that creates changes in linear motion. For rotational motion, the same force can cause very different results. A torque is an action that causes objects
1. I have 4 sides. My opposite sides are equal. I have 4 right angles. Which shape am I?
Which Shape? This problem gives you the chance to: identify and describe shapes use clues to solve riddles Use shapes A, B, or C to solve the riddles. A B C 1. I have 4 sides. My opposite sides are equal.
DWG 001. Blueprint Reading. Line Standards Drawing Symbols. Instructor Guide
DWG 001 Blueprint Reading Line Standards Drawing Symbols Instructor Guide Module Purpose Introduction The purpose of the Blueprint Reading modules is to introduce students to production drawings and blueprint
Elements of a graph. Click on the links below to jump directly to the relevant section
Click on the links below to jump directly to the relevant section Elements of a graph Linear equations and their graphs What is slope? Slope and y-intercept in the equation of a line Comparing lines on
Inclined Plane: Distance vs. Force
1a Inclined Plane: Distance vs. Force Look at the inclined plane model you built for Card 2. It s a ramp, so it s easy to slide or roll things up and down it. As you noticed, it is a little more difficult
Chapter 9. Systems of Linear Equations
Chapter 9. Systems of Linear Equations 9.1. Solve Systems of Linear Equations by Graphing KYOTE Standards: CR 21; CA 13 In this section we discuss how to solve systems of two linear equations in two variables
Circuit diagrams and symbols (1)
Circuit diagrams and symbols (1) Name: Circuit Symbols We remember how we put the circuits together by using a diagram or drawing a sketch. In order to save time and ensure that sketches are accurate,
To draw a line. To create a construction line by specifying two points
Drawing Lines, Polygons and Rectangles The line is the basic object in AutoCAD. You can create a variety of lines: single lines, multiple line segments with and without arcs, multiple parallel lines, and
Procedure for Graphing Polynomial Functions
Procedure for Graphing Polynomial Functions P(x) = a n x n + a n-1 x n-1 + + a 1 x + a 0 To graph P(x): As an example, we will examine the following polynomial function: P(x) = 2x 3 3x 2 23x + 12 1. Determine
Pythagoras Theorem. Page I can... 1... identify and label right-angled triangles. 2... explain Pythagoras Theorem. 4... calculate the hypotenuse
Pythagoras Theorem Page I can... 1... identify and label right-angled triangles 2... eplain Pythagoras Theorem 4... calculate the hypotenuse 5... calculate a shorter side 6... determine whether a triangle
Tessellating with Regular Polygons
Tessellating with Regular Polygons You ve probably seen a floor tiled with square tiles. Squares make good tiles because they can cover a surface without any gaps or overlapping. This kind of tiling is
Using Linear Programming in Real-Life Problems
Name Date A C T I V I T Y 4 Instructions Using Linear Programming in Real-Life Problems Mr. Edwards is going to bake some cookies for his algebra class. He will make two different kinds, oatmeal-raisin
Lydia. (Acts 16:11-15) Spark Resources: Spark Story Bibles, Supplies: None. Spark Resources: Spark Bibles, Spark Bible Stickers
BIBLE SKILLS & GAMES LEADER GUIDE Lydia (Acts 16:11-15) Age-Level Overview Age-Level Overview Open the Bible Activate Faith Lower Elementary Workshop Focus: We can be good listeners. Lydia Says: Kids respond
Plotting Ordered Pairs on a Four Quadrant Grid Grade Five
Ohio Standards Connection Geometry and Spatial Sense Benchmark C Specify locations and plot ordered pairs on a coordinate plane. Indicator 6 Extend understanding of coordinate system to include points
Bar Graphs and Dot Plots
CONDENSED L E S S O N 1.1 Bar Graphs and Dot Plots In this lesson you will interpret and create a variety of graphs find some summary values for a data set draw conclusions about a data set based on graphs
The University of Texas at Austin. Gravity and Orbits
UTeach Outreach The University of Texas at Austin Gravity and Orbits Time of Lesson: 60-75 minutes Content Standards Addressed in Lesson: TEKS6.11B understand that gravity is the force that governs the
CATIA Wireframe & Surfaces TABLE OF CONTENTS
TABLE OF CONTENTS Introduction... 1 Wireframe & Surfaces... 2 Pull Down Menus... 3 Edit... 3 Insert... 4 Tools... 6 Generative Shape Design Workbench... 7 Bottom Toolbar... 9 Tools... 9 Analysis... 10
Unit 6 Trigonometric Identities, Equations, and Applications
Accelerated Mathematics III Frameworks Student Edition Unit 6 Trigonometric Identities, Equations, and Applications nd Edition Unit 6: Page of 3 Table of Contents Introduction:... 3 Discovering the Pythagorean
Presents. AccuDraw. Instructor Pam Roberts [email protected] www.cadassist.com
Presents AccuDraw Instructor Pam Roberts [email protected] www.cadassist.com ACCUDRAW AccuDraw gives user an easy way to input accurate points. By default with MicroStation V8 AccuDraw will automatically
Unit 8 Angles, 2D and 3D shapes, perimeter and area
Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest
Ideal Cable. Linear Spring - 1. Cables, Springs and Pulleys
Cables, Springs and Pulleys ME 202 Ideal Cable Neglect weight (massless) Neglect bending stiffness Force parallel to cable Force only tensile (cable taut) Neglect stretching (inextensible) 1 2 Sketch a
x 2 + y 2 = 1 y 1 = x 2 + 2x y = x 2 + 2x + 1
Implicit Functions Defining Implicit Functions Up until now in this course, we have only talked about functions, which assign to every real number x in their domain exactly one real number f(x). The graphs
A. The answer as per this document is No, it cannot exist keeping all distances rational.
Rational Distance [email protected] www.unsolvedproblems.org: Q. Given a unit square, can you find any point in the same plane, either inside or outside the square, that is a rational distance from
Area and Arc Length in Polar Coordinates
Area and Arc Length in Polar Coordinates The Cartesian Coordinate System (rectangular coordinates) is not always the most convenient way to describe points, or relations in the plane. There are certainly
What is Assessment? William Slattery Wayne State University
What is Assessment? William Slattery Wayne State University Assessment Assessment is the process of observing and measuring learning. Assessments provide faculty with a better understanding of what your
Name Partners Date. Energy Diagrams I
Name Partners Date Visual Quantum Mechanics The Next Generation Energy Diagrams I Goal Changes in energy are a good way to describe an object s motion. Here you will construct energy diagrams for a toy
Trigonometry Review with the Unit Circle: All the trig. you ll ever need to know in Calculus
Trigonometry Review with the Unit Circle: All the trig. you ll ever need to know in Calculus Objectives: This is your review of trigonometry: angles, six trig. functions, identities and formulas, graphs:
Jesus Teaches About Heaven
John 14 1 Do not let your hearts be troubled. Trust in God; trust also in me. 2 In my Father s house are many rooms; if it were not so, I would have told you. I am going there to prepare a place for you.
Handwriting. Good handwriting (i.e., legible writing done by hand whether it is. Teaching Printing
Handwriting Good handwriting (i.e., legible writing done by hand whether it is printed or cursive) is an important life skill that all students should develop. It allows writers to be fluent and to communicate
Phases of the Moon. Preliminaries:
Phases of the Moon Sometimes when we look at the Moon in the sky we see a small crescent. At other times it appears as a full circle. Sometimes it appears in the daylight against a bright blue background.
Parallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.
CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes
Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern.
INTEGERS Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe
Geometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment
Geometry Chapter 1 Section Term 1.1 Point (pt) Definition A location. It is drawn as a dot, and named with a capital letter. It has no shape or size. undefined term 1.1 Line A line is made up of points
Module 8 Lesson 4: Applications of Vectors
Module 8 Lesson 4: Applications of Vectors So now that you have learned the basic skills necessary to understand and operate with vectors, in this lesson, we will look at how to solve real world problems
Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20
Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding
Algebra I Notes Relations and Functions Unit 03a
OBJECTIVES: F.IF.A.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element
DIRECTIONS FOR SOLVING THE 5x5x5 (Professor) CUBE
DIRECTIONS FOR SOLVING THE 5x5x5 (Professor) CUBE These instructions can be used to solve a 5x5x5 cube, also known as the professor cube due to its difficulty. These directions are a graphical version
1. What are the four laws that work with the law of gravity to make an airplane fly?
CHAPTER 1 YOUR WORDS HAVE POWER In the introduction to The Law of Confession, Dr. Bill Winston spoke of laws. He said a law is a principle based on the predictable consequences of an act, meaning a certain
Microsoft Office 2010 Publisher
Page 1 of 7 Microsoft Office 2010 Publisher Getting Started with Microsoft Office Publisher 2010 Microsoft Publisher is a program used for the creation of simple publications such as brochures, greeting
Contract of Employment
Contract of Employment Age Group: Young Adults/ Adults Level: Entry 3 and lower Level 1 Time: 1 hour Skill focus: Reading, the language of contracts Sub skills: Reading for specific meaning. Materials: