Unit #9: Coordinate Geometry

Trapezoids

Coordinate Geometry “Tool Box”

Midpoint

Distance

Coordinate Geometry Proof

Unit #9 Test Review

Name:__________________ Day ___ Per ___

Geometry Lab Trapezoids

1) Using the word box, label the diagram below:

2) Things to know about an Isosceles Trapezoid:

Leg Base

Median

The Median (aka mid-segment):

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.

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.

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 mR. 13) Find W.

Coordinate Geometry Tool Box

Slope Formula:

Used to show:

Distance Formula:

Used to show:

Midpoint Formula:

Used to show:

Name: __________________________________ Day __ Per __

Geometry Lab 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).

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?

Name: _________________________ Day __ Per __

Geometry Lab 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).

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 ?

Name: _________________________________ Day __ Per __ Geometry Lab 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 ̅̅ ̅̅ .

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.

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.

Name: _____________________________________ Day ___ Per ___ Geometry Lab 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.

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.)

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 = -3

4. 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?

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) Quadrilateral SONG has vertices S(2,3), O(10,3), N(10,-1), and G(2,-1). Prove

quadrilateral SONG is a rectangle.