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.