Unit #9: Coordinate Geometry

Transcription

1 Unit #9: Coordinate Geometry Trapezoids Coordinate Geometry Tool Box Midpoint Distance Coordinate Geometry Proof Unit #9 Test Review

2 Name: Geometry Lab Day Per Trapezoids 1) Using the word box, label the diagram below: Leg Base Median 2) Things to know about an Isosceles Trapezoid: The Median (aka mid-segment):

3 3) In isosceles trapezoid ABCD, AB DC. If AD = 3x + 4 and BC = x + 12, solve for x. 4) If RT is the median of trapezoid ABCD. Find the length of RT. 5) In the accompanying diagram, isosceles trapezoid CDEF has bases of lengths 6 and 12 and an altitude of length 4. Find CD.

4 6) In trapezoid ABCD, AB CD. If AB = 2 and CD = 50, what is measure of the median MN? 7) Find the length of the median of a trapezoid if the lengths of the two bases are 20 and 46 inches. 8) In isosceles trapezoid RSTU, RS = 8x + 5 and TU = 2x +29. Express the length of the median QP in terms of x. (Hint: Draw a picture) 9) In isosceles trapezoid ABCD, diagonal AC is 2x+10 and diagonal BD is 86+x. Find the length of each diagonal.

5 10) In isosceles trapezoid DEGF, DE = 20, FG = 30 and DH = 12. Find the length of GD. 11) EF is the mid-segment of trapezoid ABCD. EF = 25 and AD = 40. Find BC. 12) Find the m R. 13) Find W.

6 Coordinate Geometry Tool Box Slope Formula: Used to show: Distance Formula: Used to show: Midpoint Formula: Used to show:

7 Name: Geometry Lab Day Per Coordinate Geometry-Midpoint Midpoint Formula: (Use when you are given the two end points), Use when given ONE endpoint and the Midpoint: Ex: 1. Find the midpoint of the segment connecting the points (6,4) and (3,-4). 2. The coordinates of A are ( 9,2) and the coordinates of G are (3,14). What are the coordinates of the midpoint of AG? 3. What is the midpoint of the line segment that joins points (4, 2) and ( 2,5)? 4. Find the midpoint of the segment connecting the points (a,b) and (3a,c).

8 5. Line segment AB has endpoints A(2, 3) and B( 4,6). What are the coordinates of the midpointof AB? 6. A line segment has endpoints A(7,-1) and B(-3,3). What are the coordinates of the midpoint of AB? 7. In circle O, diameter RS has endpoints R(3a, 2b-1) and S(a-6, 4b+5). Find the coordinates of point O, in terms of a and b. Express your answer in simplest form. 8. M is the midpoint of AB. The coordinates of A are (-2,3) and the coordinates of M are (1,0). Find the coordinates of B. 9. M is the midpoint of AB. If the coordinates of A are (-1,5) and the coordinates of M are (3,3), what are the coordinates of B? 10. A line segment on the coordinate plane has endpoints (2,4) and (4,y). The midpoint of the segment is point (3,7). What is the value of y? 11. The midpoint M of line segment AB has coordinates (-3,4). If point A is the origin, (0,0), what are the coordinates of point B? 12. The coordinates of the midpoint of AB are (2,4) and the coordinates of point B are (3,7). What are the coordinates of point A?

9 Name: Geometry Lab Day Per Coordinate Geometry-Distance Distance Formula: 1. The coordinates of point R are (-3,2) and the coordinates of point T are (4,1). What is the length of RT? 2. What is the length of the radius of a circle whose diameter has end points of (1,0) and (5,4)? 3. Find the length of the line segment whose endpoints are (-3, 4) and (5,4). 4. Determine the length of if the coordinates of A are ( 2,-3) and of B( 2,7).

10 5. is the diameter of a circle with coordinates M(7,-2) and Z(1,5). Find the length of the radius. 6. What is the length of the line segment whose endpoints are (1, -4) and (9,2)? 7. If the endpoints of AB are A(-4,5) and B(2,-5), what is the length of AB? 8. What is the distance between points A(7,3) and B(5,-1)? 9. The coordinates of point R are (-3,2) and the coordinates of point T are (4,1). What is the length of RT?

11 Name: Geometry Lab Day Per Coordinate Geometry Proofs in Coordinate Geometry 1. Determine the distance between point A(-1,-3) and point B(5,5). Write an equation of the perpendicular bisector of AB? 2. Determine the distance between point M(-3,8) and point Z(7,-2). Write an equation of the perpendicular bisector of MZ. 3. Given: Trapezoid MATH M(-2,3), A( 4,3), T(6,1) and H(-4,1) find the length of the mid-segment.

12 4. The vertices of ABC are A(-7, 1), B(5, -3) and C(-3,5). Prove ABC is a right. 5. Given: A(1,6),B(7,9),C(13,6), and D(3,1) Prove: ABCD is a trapezoid 6. Prove that A(-2,2), B(1,4), C(2,8) and D(-1,6) is a parallelogram.

13 7. Prove: F(-4,1), O(2,5), U(4,2), R(-2,-2) is a rectangle. 8. Given: J ( 4,1), E ( 2, 3), N (2, 1) Prove: JEN is an isosceles right triangle. 9. Prove that A(-3,2), B(-2,6), C(2,7) and D(1,3) is a rhombus.

14 Name: Geometry Lab Day Per Unit #9 Test Review 1) M is the midpoint of line segment TP. The coordinates of P are (-8, 4) and the coordinates of M are (-1,-2). Find the coordinates of T. 2) Circle O has a center at (3,-5) and a diameter AB. If the coordinates of A are (-3,6), what are the coordinates of B? 3) Find the midpoint of the segment connecting the points (4, 8) and (-2,1). 4) Find the midpoint of the segment connecting the points (3M,3E-1) and (M-6, 5E +4) 5) In circle O, diameter RS has endpoints R(3a, 2b-1) and S(a-6, 4b+5). Find the coordinates of point O, in terms of a and b. Express your answer in simplest form. 6) Determine the perimeter of a square, whose side measures 12. Express your answer in simplest radical form.

15 7) Find the perimeter of a rhombus, whose side measures 3 20 ( Express your answer in simplest radical form). 8) What is the length of the line segment that joins points (6,-2) and (9,4)? Express your answer in simplest radical form. 9) Determine the distance between points G (-4,7) and Z(-7,5). 10) Find the distance between point A(-9,-6) and Z(6,3). (Round your answer to the nearest tenth.)

16 11) In isosceles trapezoid ABCD AB//DC. If AD = 3x+4 and BC = x+12, find the length of AD. 12) A. Find the length of RT. B. Given isosceles trapezoid ABCD, find the height of the trapezoid. 13) In isosceles trapezoid ABCD, AB // CD, AB = 18, CD = 26 and AD = 5. Find the length of the altitude of ABCD. 14) A. In triangle MAP, the slope of MA = B. In triangle BOY, the slope of the Determine the slope of the altitude altitude from vertex O to BY is 5. from vertex P to MA. What is the slope to BY?

17 15) Write the equation of the perpendicular bisector of C(-5,2) and D(1,5). 16) Write the equation of the perpendicular bisector of T(4,2) and Y(-4,4). 17) Quadrilateral LOVE has vertices L(2,2), O(5,2), V(6,-2), and E(3,-2). Prove quadrilateral LOVE is a parallelogram.

18 18) Quadrilateral SONG has vertices S(2,3), O(10,3), N(10,-1), and G(2,-1). Prove quadrilateral SONG is a rectangle.