Download ExamView - Parallel and Perpendicular Lines Unit Review.tst

Name: ________________________ Class: ___________________ Date: __________
ID: A
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?
5
3
c. −
a.
3
5
3
5
b.
d. −
5
3
____
2. Which graph could be used to find the solution to the following system of equations?
y = −x + 2
y=x
____
a.
c.
b.
d.
2
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?
1
25
a. y = 2x + 5
c. y = x +
2
2
1
25
b. y = 2x − 5
d. y = − x −
2
2
1
Name: ________________________
____
ID: A
←→
←→
4. The diagram below illustrates the construction of PS parallel to RQ through point P.
Which statement justifies this construction?
c. PR ≅ RQ
a. m∠1 = m∠2
b. m∠1 = m∠3
d. PS ≅ RQ
____
5. Find m∠ABC .
a. m∠ABC = 40º
b. m∠ABC = 45º
____
c. m∠ABC = 35º
d. m∠ABC = 50º
2
6. Given the system of equations: y = x − 4x
x=4
The number of points of intersection is
a. 1
b. 2
c. 3
d. 0
2
Name: ________________________
____
____
ID: A
2
7. What is the slope of a line perpendicular to the line whose equation is y = − x − 5?
3
3
2
a. −
c.
2
3
2
3
b. −
d.
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
c.
5
d. −3
−5
b. − 2
____
1
−3
11. Based on the diagram below, which statement is true?
a. a Ä b
b. a Ä c
c. b Ä c
d. d Ä e
3
Name: ________________________
ID: A
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.
2
2x − 4x = y + 1
x+y=1
4
ID: A
Parallel & Perpendicular Lines Unit Review
Answer Section
MULTIPLE CHOICE
1. ANS: B
A
5
so the slope of this line is −
Perpendicular lines have
B
3
slope that are the opposite and reciprocal of each other.
The slope of a line in standard form is −
PTS: 2
REF: fall0828ge
TOP: Parallel and Perpendicular Lines
2. ANS: C
STA: G.G.62
PTS: 2
REF: fall0805ge
TOP: Quadratic-Linear Systems
3. ANS: B
STA: G.G.70
A
−2
= 2. A parallel line
The slope of a line in standard form is − , so the slope of this line is
B
−1
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
PTS:
TOP:
4. ANS:
TOP:
2
REF: fall0812ge
Parallel and Perpendicular Lines
A
PTS: 2
Constructions
STA: G.G.65
REF: fall0807ge
1
STA: G.G.19
ID: A
5. ANS: C
(x)° = (3x − 70)°
0 = 2x − 70
70 = 2x
35 = x
m∠ABC = 3x − 70
m∠ABC = 3(35) − 70 = 35°
Corresponding angles are congruent.
Subtract x from both sides.
Add 70 to both sides.
Divide both sides by 2.
Substitute 35 for x. Simplify.
Feedback
A
B
C
D
If two parallel lines are cut by a transversal, then the pairs of corresponding
angles are congruent.
Use the Corresponding Angles Postulate.
Correct!
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
TOP: 7-2 Parallel and Perpendicular Lines
6. ANS: A
STA: 8.G.4
2
2
y = x − 4x = (4) − 4(4) = 0. (4, 0) is the only intersection.
PTS: 2
REF: 060923ge
STA: G.G.70
TOP: Quadratic-Linear Systems
7. ANS: D
2
2
The slope of y = − x − 5 is − . Perpendicular lines have slope that are opposite reciprocals.
3
3
PTS: 2
REF: 080917ge
TOP: Parallel and Perpendicular Lines
STA: G.G.62
2
ID: A
8. ANS: D
x + 6y = 12
6y = −x + 12
1
y= − x+2
6
m=−
3(x − 2) = −y − 4
−3(x − 2) = y + 4
m = −3
1
6
PTS: 2
REF: 011119ge
STA:
TOP: Parallel and Perpendicular Lines
9. ANS: B
PTS: 2
REF:
TOP: Parallel Lines and Transversals
10. ANS: C
y2 − y1
Use the slope formula.
m=
x2 − x1
(−4) − (−6)
Substitute (5, − 6) for (x 1 ,
m=
(−1) − (5)
2
1
Simplify.
m=
= −3
−6
G.G.63
061007ge
STA: G.G.35
y 1 ) and (−1, − 4) for (x 2 , y 2 ).
Feedback
A
B
C
D
Divide the difference in y-values by the difference in x-values.
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.
Correct!
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.
PTS: 2
REF: 080901ge
TOP: Parallel Lines and Transversals
STA: G.G.35
3
ID: A
SHORT ANSWER
12. ANS:
y = −2x + 14. The slope of 2x + y = 3 is
−A −2
=
= −2. y = mx + b
.
1
B
4 = (−2)(5) + b
b = 14
PTS: 2
REF: 060931ge
TOP: Parallel and Perpendicular Lines
13. ANS:
STA: G.G.65
PTS: 4
REF: 061137ge
TOP: Quadratic-Linear Systems
STA: G.G.70
4