examview - parallel and perpendicular lines unit revie · parallel & perpendicular ... which...

Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Parallel & Perpendicular Lines Unit Review

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. What is the slope of a line perpendicular to the line whose equation is 5x + 3y = 8?

a.5

3c. −

3

5

b.3

5d. −

5

3

____ 2. Which graph could be used to find the solution to the following system of equations?

y = −x + 2

y = x2

a. c.

b. d.

____ 3. What is the equation of a line that passes through the point (−3,−11) and is parallel to the line

whose equation is 2x − y = 4?

a. y = 2x + 5 c. y =1

2x +

25

2

b. y = 2x − 5 d. y = −1

2x −

25

2

Name: ________________________ ID: A

2

____ 4. The diagram below illustrates the construction of PS→←

parallel to RQ→←

through point P.

Which statement justifies this construction?

a. m∠1 = m∠2 c. PR ≅ RQ

b. m∠1 = m∠3 d. PS ≅ RQ

____ 5. Find m∠ABC .

a. m∠ABC = 40º c. m∠ABC = 35º

b. m∠ABC = 45º d. m∠ABC = 50º

____ 6. Given the system of equations: y = x2

− 4x

x = 4

The number of points of intersection is

a. 1 c. 3

b. 2 d. 0

Name: ________________________ ID: A

3

____ 7. What is the slope of a line perpendicular to the line whose equation is y = −2

3x − 5?

a. −3

2c.

2

3

b. −2

3d.

3

2

____ 8. The two lines represented by the equations below are graphed on a coordinate plane.

x + 6y = 12

3(x − 2) = −y − 4

Which statement best describes the two lines?

a. The lines are parallel.

b. The lines are the same line.

c. The lines are perpendicular.

d. The lines intersect at an angle other than 90°.

____ 9. A transversal intersects two lines. Which condition would always make the two lines parallel?

a. Vertical angles are congruent.

b. Alternate interior angles are congruent.

c. Corresponding angles are supplementary.

d. Same-side interior angles are complementary.

____ 10. Find the slope of the line that contains (5, − 6) and (−1, − 4).

a. −2

5c. −

1

3

b. −5

2d. −3

____ 11. Based on the diagram below, which statement is true?

a. a Ä b c. b Ä c

b. a Ä c d. d Ä e

Name: ________________________ ID: A

4

Short Answer

12. Find an equation of the line passing through the point (5, 4) and parallel to the line whose equation

is 2x + y = 3.

Answer:_________________________________

13. Solve the following system of equations graphically.

2x2

− 4x = y + 1

x + y = 1

ID: A

1

Parallel & Perpendicular Lines Unit Review

Answer Section

MULTIPLE CHOICE

1. ANS: B

The slope of a line in standard form is −A

B so the slope of this line is −

5

3 Perpendicular lines have

slope that are the opposite and reciprocal of each other.

PTS: 2 REF: fall0828ge STA: G.G.62

TOP: Parallel and Perpendicular Lines

2. ANS: C


TOP: Quadratic-Linear Systems

3. ANS: B

The slope of a line in standard form is −A

B, so the slope of this line is

−2

−1= 2. A parallel line

would also have a slope of 2. Since the answers are in slope intercept form, find the y-intercept:

y = mx + b

−11 = 2(−3) + b

−5 = b



4. ANS: A PTS: 2 REF: fall0807ge STA: G.G.19

TOP: Constructions

ID: A

2

5. ANS: C(x)° = (3x − 70)° Corresponding angles are congruent.0 = 2x − 70 Subtract x from both sides.70 = 2x Add 70 to both sides.35 = x Divide both sides by 2.

m∠ABC = 3x − 70

m∠ABC = 3(35) − 70 = 35° Substitute 35 for x. Simplify.

Feedback

A If two parallel lines are cut by a transversal, then the pairs of corresponding

angles are congruent.

B Use the Corresponding Angles Postulate.

C Correct!

D First, set the measures of the corresponding angles equal to each other. Then,

solve for x and substitute in the expression (3x - 70).

PTS: 1 DIF: Advanced NAT: 8.3.3.g STA: 8.G.4

TOP: 7-2 Parallel and Perpendicular Lines

6. ANS: A

y = x2

− 4x = (4)2

− 4(4) = 0. (4, 0) is the only intersection.

PTS: 2 REF: 060923ge STA: G.G.70


7. ANS: D

The slope of y = −2

3x − 5 is −

2

3. Perpendicular lines have slope that are opposite reciprocals.



ID: A

3

8. ANS: D

x + 6y = 12

6y = −x + 12

y = −1

6x + 2

m = −1

6

3(x − 2) = −y − 4

−3(x − 2) = y + 4

m = −3



9. ANS: B PTS: 2 REF: 061007ge STA: G.G.35

TOP: Parallel Lines and Transversals

10. ANS: C

m =

y2 − y1

x 2 − x1

Use the slope formula.

m =(−4) − (−6)

(−1) − (5)

Substitute (5, − 6) for (x 1, y1) and (−1, − 4) for (x 2, y2).

m =2

−6= −

1

3

Simplify.

Feedback

A Divide the difference in y-values by the difference in x-values.

B First, substitute the coordinates of the first point into (x1, x2) and the coordinates

of the second point into (y1, y2) of the slope formula. Then, simplify.

C Correct!

D Use the slope formula.

PTS: 1 DIF: Basic REF: Page 320

OBJ: 5-4.1 Finding Slope by Using the Slope Formula NAT: 12.5.2.b

STA: A.A.33 TOP: 5-4 The Slope Formula

11. ANS: D

The marked 60º angle and the angle above it are on the same straight line and supplementary. This

unmarked supplementary angle is 120º. Because the unmarked 120º angle and the marked 120º

angle are alternate exterior angles and congruent, d Ä e.


TOP: Parallel Lines and Transversals

ID: A

4

SHORT ANSWER

12. ANS:

y = −2x + 14. The slope of 2x + y = 3 is −A

B=

−2

1= −2. y = mx + b

4 = (−2)(5) + b

b = 14

.



13. ANS:



examview - parallel and perpendicular lines unit revie · parallel & perpendicular ... which...

Documents