Test Corrections for Unit 1 Test

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able to fully and accurately explain the how and why of each problem. These test corrections take a long time

to complete, however, they can earn you up to 1/2 of the points back that you lost on the Unit 1 test. If you

take advantage of this opportunity you will not only understand the material better, but you will also improve

your grade in the class.

1. Trapezoid ABCD has coordinates A(0, 9),

B(12, 9), C(8, 4), and D(0, 4).

a) Using coordinate geometry, show that−−−AD

is not parallel to−−−BC.

b) Find the area of trapezoid ABCD.

c) Find the perimeter of ABCD to the

nearest integer.

d) Find m∠ABC to the nearest degree.

2. Point P has coordinates (−12, 5). What is its

distance from the origin?

3. Find an equation of the line passing through

the point (6, 5) and perpendicular to the line

whose equation is 2y + 3x = 6.

4. Square ABCD has vertices A(−2,−3), B(4,−1),C(2, 5), and D(−4, 3). What is the length of a

side of the square?

A. 2√5 B. 2

√10 C. 4

√5 D. 10

√2

5. In the diagram below, quadrilateral ABCD

has vertices A(−5, 1), B(6,−1), C(3, 5), andD(−2, 7).

What are the coordinates of the midpoint of

diagonal−−−AC?

A. (−1, 3) B. (1, 3)

C. (1, 4) D. (2, 3)

6. Find the distance between the points (−1, 5)and (−7, 3).

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7. Line ` passes through the point (5, 3) and is

parallel to line k whose equation is 5x + y = 6.

An equation of line ` is

A. y =1

5x + 2 B. y = −5x + 28

C. y =1

5x − 2 D. y = −5x − 28

8. In the coordinate plane, the points (2, 2) and

(2, 12) are the endpoints of a diameter of a

circle. What is the length of the radius of the

circle?

A. 5 B. 6 C. 7 D. 10

9. What is an equation of the line that passes

through the point (7, 3) and is parallel to the

line 4x + 2y = 10?

A. y =1

2x − 1

2B. y = −1

2x +

13

2

C. y = 2x − 11 D. y = −2x + 17

10. What is the length of the line segment joining

the points (−3,−4) and (2,−5)?

11. In parallelogram ABCD, the coordinates of A

are (4, 3) and the coordinates of the midpoint

of diagonal−−−AC are (2, 5). What are the

coordinates of C ?

12. The coordinates of the endpoints of the

diameter of a circle are (3, 7) and (−5, 3).Find the coordinates of the center of the circle.

13. The coordinates of A and B are (2a, 4b) and

(8a, 6b), respectively. Express in terms of a

and b, the coordinates of the midpoint of−−−AB.

14. Trapezoid ABCD has coordinates A(−6, 0),B(17, 0), C(2, 8), and D(0, 8). Find the

a) area of trapezoid ABCD

b) perimeter of trapezoid ABCD

c) measure of ∠B to the nearest degree

15. The midpoint of−−−AB is M, the coordinates of

A are (a, b), and the coordinates of B are

(a + 4, 5b). What are the coordinates of M?

A. (2, 2b) B. (a + 2, 3b)

C. (2a + 4, 6b) D.

(

a + 4

2,

5b

2

)

16. Triangle HKL has vertices H(−7, 2), K(3,−4),and L(5, 4). The midpoint of

−−−HL is M and the

midpoint of−−−LK is N.

Determine and state the coordinates of

points M and N.

Justify the statement:−−−−MN is parallel to

−−−−HK.

[The use of the set of axes below is optional.]

page 2 Test Corrections for Unit 1 Test

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17. The coordinates of the vertices of ^ABC are

A(−4, 1), B(4, 9), C(9,−2). Point M(1, 6) lies

on−−−AB.

a) Show by means of coordinate geometry

that−−−−CM ⊥ −−−AB.

b) Find, to the nearest degree, the measure

of angle A.

18. The graph of the equation y =1

3x + 2 is

perpendicular to the graph of the equation

A. y =1

3x + 5 B. 3y = x + 2

C. y = 3x + 5 D. y = −3x + 2

19. Which point is farthest from the origin?

A. (0,−5) B. (6, 0)

C. (3, 4) D. (4, 2)

20. Triangle ABC has vertices A(−2, 1), B(5, 5),and C(−1,−7).

a) Show that ^ABC is isosceles.

b) Find the length of the altitude drawn

from A to−−−BC.

c) Using the results obtained in parts a

and b, find, to the nearest degree, the

measure of a base angle of this triangle.

21. Which equation represents a line parallel to the

line whose equation is 2y = 3x + 6?

A. 3y = 2x + 6 B. 2y = −3x + 6

C. y =2

3x + 1 D. y =

3

2x − 4

22. Which equation represents a line that is parallel

to the line whose equation is 2x + 3y = 12?

A. 6y − 4x = 2 B. 6y + 4x = 2

C. 4x − 6y = 2 D. 6x + 4y = −2

23. Segment AB is the diameter of a circle whose

center is the point (2, 5). If the coordinates of

A are (1, 3), find the coordinates of B.

24. Points A(5, 3) and B(7, 6) lie on←→AB. Points

C(6, 4) and D(9, 0) lie on←→CD. Which

statement is true?

A.←→AB ‖ ←→CD

B.←→AB ⊥ ←→CD

C.←→AB and

←→CD are the same line.

D.←→AB and

←→CD intersect, but are not

perpendicular.

25. Which equation represents a line that is parallel

to the line whose equation is 3x − 2y = 7?

A. y = −32x + 5 B. y = −2

3x + 4

C. y =3

2x − 5 D. y =

2

3x − 4

26. Which line is perpendicular to the line whose

equation is 5y + 6 = −3x?

A. y = −5

3x + 7 B. y =

5

3x + 7

C. y = −3

5x + 7 D. y =

3

5x + 7

page 3 Test Corrections for Unit 1 Test

27. Write an equation of the perpendicular bisector

of the line segment whose endpoints are

(−1, 1) and (7,−5). [The use of the grid

below is optional.]

28. Which equation represents the line that passes

through the point (0, 1) and is parallel to the

line whose equation is 3x + y = 5?

A. 3x + y = 3 B. 3x + y = 1

C. 3x + y = 0 D. 3x + y = −1

29. Write an equation of the line that passes

through the point (6,−5) and is parallel to the

line whose equation is 2x − 3y = 11.

30. What is an equation of the line that passes

through the point (3,−1) and has a slope of 2?

A. y = 2x + 5 B. y = 2x − 1

C. y = 2x − 4 D. y = 2x − 7

31. What is the equation of the line that is

perpendicular to the line y − 2x = 4 and passes

through point (2, 4)?

A. y =1

2x + 4 B. y = −1

2x + 5

C. y =1

2x + 5 D. y = −2x + 5

page 4 Test Corrections for Unit 1 Test

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