Plot Integers on a Number Line. Find the Distance Between Points on a Number Line. Plot Points on a Coordinate Grid. PDF Proof
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1 00-013_Ch01_09731_ML7.indd Page 7/5/07 7:0:13 PM remote /Volumes/ju105/MHHE0/indd%0/ch01 Plot Integers on a Number Line Integers include positive numbers, negative numbers, and zero. Integers can be shown on a number line. negative integers positive integers 0 is neither positive nor negative +1 is read as positive one. 1 is read as negative one. 1. For each letter on the number lines, identif the integer. b) P 10 N 0 +5 Q +15 a) D C Find the Distance etween Points on a Number Line The distance between two points on a number line can be determined b counting What is the distance between the two numbers placed on a number line? a) and 10 b) - and -8 c) -1 and -3 d) +7 and -3 e) -1 and 1 3. Draw an integer number line. a) Mark the point that is four less than zero. Label it. b) Mark the point that is three more than zero. Label it. c) Mark the point that is 7 more than -. Label it C. Plot Points on a Coordinate Grid The points (1, 3), (5, ), C(, ), D(, 0), and E(0, 1) can be plotted on a coordinate grid. Each point is named with an ordered pair. (1, 3) C(, ) (5, ) -coordinate (1, 3) -coordinate 0 E(0, 1) D(, 0) 8 MHR Chapter 1: Coordinates and Design
2 00-013_Ch01_09731_ML7.indd Page 3 7/5/07 7:0:1 PM remote /Volumes/ju105/MHHE0/indd%0/ch01. State an ordered pair for each point on the coordinate grid. 0 H G I F J F G H I J Identif Transformations transformation moves one geometric figure onto another. Three tpes of transformations are translation, reflection, and rotation. translation is a slide. translation arrow reflection is a mirror image. mirror line rotation is a turn. angle of rotation turn centre 5. What is a transformation that moves Figure onto Figure? a) b) c) Identif ngles of Rotation figure can be turned or rotated an number of degrees The rotation can be clockwise or counterclockwise. clockwise counterclockwise. What is the angle of rotation for each of the following rotations? Is the rotation clockwise or counterclockwise? a) b) c) d) Get Read MHR 3
3 00-013_Ch01_09731_ML7.indd Page 7/5/07 7:0:18 PM remote /Volumes/ju105/MHHE0/indd%0/ch The Cartesian Plane MathLinks 7, pages 11 Ke Ideas Review Choose from the following terms to complete #1 and #. I II III IV Cartesian origin plane quadrant -ais -ais 1. Complete each statement. a) n ordered pair (, ) is used to locate an point on a plane. b) ll points located within the same have the same signs for their -coordinates and the same signs for their -coordinates.. Fill in the blanks on the diagram. Quadrant Quadrant 0 Quadrant Quadrant Practise and ppl 3. What are the coordinates of each point shown on the coordinate grid? E 0 D F C. Identif the letter on the coordinate grid that matches each ordered pair. S Q 0 V R T P C E D F a) (0, 5) b) (, 1) c) (, ) d) (, ) e) ( 3, 0) f) (, 3) MHR Chapter 1: Coordinates and Design
4 00-013_Ch01_09731_ML7.indd Page 5 7/5/07 7:0:18 PM remote /Volumes/ju105/MHHE0/indd%0/ch01 5. a) Plot each ordered pair on the coordinate grid: (, 3), (, ), C(1, ), D(, ), E(, 3). 7. a) Create a rectangle b plotting two points in quadrant I and two points in quadrant IV, and connecting the points. 0 0 b) Connect to, to C, C to D, and D to E. What shape did ou create?. a) Create a square b plotting and connecting points P(5, 1), Q(5, 5), R( 1, 5), and S( 1, 1). b) Write the coordinates of each verte on the grid. c) What is the length of each side of the rectangle? 8. a) Create an isosceles right triangle that has each verte in a different quadrant. 0 0 b) What is the area of the square? Show how ou know. b) Write the coordinates of each verte on the grid. c) What is the perimeter of the square? Show how ou know. c) Show how ou know the triangle is isosceles. 1.1 The Cartesian Plane MHR 5
5 00-013_Ch01_09731_ML7.indd Page 7/5/07 7:0:19 PM remote /Volumes/ju105/MHHE0/indd%0/ch01 1. Create Designs MathLinks 7, pages 1 17 Ke Ideas Review 1. What steps should ou take to draw a design on a coordinate grid? Write the step number from column that matches each description in column. a) Connect the vertices to make the design. b) Plot the vertices of the design. c) Colour the design, if it has colour. d) Identif the vertices and name their coordinates. Step 1 Step Step 3 Step. figure has the following coordinates: R(, ), S( 5, ), T( 5, 1), U(, 1). a) Label the -ais from at least to. b) Label the -ais from at least to. Practise and ppl 3. Write the coordinates of the vertices of figures E, F, G, and H on the grid.. a) For the following design, write the coordinates of the vertices on the grid. G E F 0 H b) Describe the steps ou would follow to cop the design. MHR Chapter 1: Coordinates and Design
6 00-013_Ch01_09731_ML7.indd Page 7 7/5/07 7:0:19 PM remote /Volumes/ju105/MHHE0/indd%0/ch01 5. a) For each of the following designs, write the coordinates of the vertices on the grid. b) Connect the dots in this order:,, C, D,, E, F, G,, H, I, J,, K, L, M,. Design Describe the design. Design 7. a) Draw a coordinate grid of quadrant I onl. 0 b) What steps would ou follow to cop each design?. a) Label the coordinate grid from to. Draw a design b plotting the following points: (0, 0), ( 1, ), C(, ), D( 1, 0), E(, 1), F(, ), G(0, 1), H(1, ), I(, ), J(1, 0), K(, 1), L(, ), M(0, 1). b) Label the aes b s from 0 to 10. c) Plot the following points on the grid: R(, 9), S(7, 9), T(7, 1), V(, 1). d) Connect R to S, S to T, T to V, and V to R. e) What figure have ou drawn? f) List the length and width of the figure as an ordered pair (l, w). 1. Create Designs MHR 7
7 00-013_Ch01_09731_ML7.indd Page 8 7/5/07 7:0:0 PM remote /Volumes/ju105/MHHE0/indd%0/ch Transformations MathLinks 7, pages 18 9 Ke Ideas Review Choose from the following terms to complete #1. centre of rotation point transformation translation reflection rotation 1. Complete each statement. a) nother word for slide is. b) can be clockwise or counterclockwise. c) is a mirror image.. Identif each transformation. a) b) c) Practise and ppl 3. What is the translation shown in each diagram? a) b) 0 0 Translation: Translation: 8 MHR Chapter 1: Coordinates and Design
8 00-013_Ch01_09731_ML7.indd Page 9 7/5/07 7:0:0 PM remote /Volumes/ju105/MHHE0/indd%0/ch01. a) Translate figure DEFG 3 units left and units down. E D 0 G 7. The diagram shows figure MSE, its rotation image, and centre of rotation R. M' S' F 0 E R E' ' b) Draw the translation arrow. S M c) Write the coordinates of the translation image on the grid. 5. a) Is figure S P T a reflection image of figure SPT in the line of reflection l? Yes No a) Label the coordinates of MSE and M S E on the grid. b) What are the direction and angle of rotation? S P P' S' 8. The diagram shows a triangle and its rotation image. T ' T' l 0 b) How do ou know? 0. Draw the line of reflection for the parallelogram. 0 a) Label the coordinates of the centre of rotation on the grid. b) What are the direction and angle of rotation? Give more than one answer, if possible. 1.3 Transformations MHR 9
9 00-013_Ch01_09731_ML7.indd Page 10 7/5/07 7:0:1 PM remote /Volumes/ju105/MHHE0/indd%0/ch01 1. Horizontal and Vertical Distances MathLinks 7, pages Ke Ideas Review 1. Use the grid to complete each statement. a) Movement from to is called movement. b) Movement from to is called c) fter one transformation, D movement. becomes. d) fter two transformations, D becomes. D D C C 0 D C Practise and ppl. Describe the horizontal and vertical movements of point T to each of the following points. T 0 G F D E 3. Parallelogram SUVT has been translated. S T U V 0 U T V S a) D b) E c) F d) G a) Label the coordinates of S U V T on the grid. b) What are the horizontal and vertical movements of SUVT to S U V T? 10 MHR Chapter 1: Coordinates and Design
10 00-013_Ch01_09731_ML7.indd Page 11 7/5/07 7:0:1 PM remote /Volumes/ju105/MHHE0/indd%0/ch01. a) Draw a triangle with vertices C( 1, 1), D(, ), and E(, 1). Reflect CDE over the -ais. Reflect C D E over the -ais. 0 c) Translate verte T 1 unit left and 7 units down. Label this verte T. d) Translate verte S units left and units down. e) Connect D to V, V to T, T to S, and S to D. f) What one transformation of the parallelogram DVTS would have given the same result? b) Describe the horizontal and vertical change in position of C to C to C.. R 8 c) Describe the movement of the vertices in the reflection over the -ais. S 8 T 0 8 d) Label the coordinates of triangle C D E on the grid. e) Compare the coordinates of C with C. What do ou notice? 8 5. V T a) Translate the triangle 1 unit horizontall lef t, and units verticall down. b) Label the ver tices of the translated triangle on the grid. 0 D S a) Translate verte D 1 unit left and 3 units down. Label this verte D. b) Translate verte V units down. Label this verte V. c) Reflect RST over the -ais and label the triangle R S T. d) Label the ver tices of the ref lected triangle on the grid. e) Rotate RST 180 about the centre of rotation (0, 0) and label this triangle R S T. f) Label the vertices of the rotated triangle on the grid. 1. Horizontal and Vertical Distances MHR 11
11 00-013_Ch01_09731_ML7.indd Page 1 7/5/07 7:0: PM remote /Volumes/ju105/MHHE0/indd%0/ch01 Link It Together 1. a) Plot triangle PQR with vertices P( 5, 1), Q( 3, ), and R( 1, 0) on the coordinate grid. b) Translate the triangle 3 units horizontall right and units verticall down. Label the new triangle P Q R. c) Reflect triangle P Q R in the -ais to form triangle P Q R. d) Label the coordinates of the vertices of triangle P Q R on the grid. e) What are the horizontal and vertical movements from P to P, Q to Q, and R to R?. a) In quadrant I, design the shape of the first initial of our name. b) Label the coordinates of the vertices on the grid. c) Describe a reflection that would move our initial to quadrant II. Draw the reflection image. d) Describe a rotation that would move our initial to quadrant III. Draw the rotation image. e) Describe a translation that would move our initial to quadrant IV. Draw the translation image. 1 MHR Chapter 1: Coordinates and Design
12 00-013_Ch01_09731_ML7.indd Page 13 7/5/07 7:0:3 PM remote /Volumes/ju105/MHHE0/indd%0/ch01 Vocabular Link Unscramble the letters of each word. Use the clues to help ou solve the puzzles. 1. The four regions of a coordinate grid are referred to SRTUDQN as.. This transformation involves a slide along a straight line:. 0 STOTNLRIN 3. The vertical line on a coordinate grid is called a(n). SX-IY. The for the origin are (0, 0). ROENSDTCOI 5. The horizontal line on a coordinate grid is called a(n).. (n) is formed when a horizontal number line and a vertical number line cross. 7. This transformation involves a flip over a mirror line:. -IXXS TECRNSI NPLE FETINEOLRC 8. The -ais and -ais cross at the.? IRINGO 9. Translations, reflections, and rotations are all tpes FITOROSNSMTNR of. 10. (n) is a turn around a fied point. IORONTT 11. (n) is the point where two sides of a figure meet.? EEXVTR Chapter 1: Vocabular Link MHR 13
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