AnswersPARTA - EOP PGCPS GEOMETRY OC FALL2026 - 793413Slopes of Parallel and Perpendicular Lines

Slopes of Parallel and Perpendicular Lines Answers

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1
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Determine the missing information in the paragraph proof.Given: Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular. Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).Prove: The slopes of perpendicular lines are negative reciprocals.

Question illustration
A
(StartFraction d minus b Over c minus a EndFraction) (StartFraction c minus a Over negative d + b EndFraction) = negative 1
Option A
B
(StartFraction b minus a Over a + b EndFraction) (StartFraction c minus d Over negative d minus c EndFraction) = negative 1
Option B
C
(StartFraction d minus b Over c minus a EndFraction) (StartFraction c minus a Over negative d + b EndFraction) = 1
Option C
D
(StartFraction b minus a Over a + b EndFraction) (StartFraction c minus d Over negative d minus c EndFraction) = 1
Option D
2
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Which statements are true about these lines? Select three options.

A
Line RS has a slope of 6.
B
Line SW has an undefined slope.
C
Line TV has a slope of 0.
D
Lines RS and TV are parallel.
E
Line SW is perpendicular to line RS, but not to line TV.
3

A line has a slope of . Which ordered pairs could be points on a parallel line? Select two options.

Question illustration
A
(–8, 8) and (2, 2)
B
(–5, –1) and (0, 2)
C
(–3, 6) and (6, –9)
D
(–2, 1) and (3, –2)
E
(0, 2) and (5, 5)
6

Line WV is perpendicular to both line RS and line TU.

Question illustration
A
Line TU is parallel to line RS.
B
Line TU is perpendicular to line RS.
C
Line TU has no slope.
D
Line TU has a slope of –5.
11

A line has a slope of . Which ordered pairs could be points on a line that is perpendicular to this line? Select two options.

Question illustration
A
(–2, 0) and (2, 5)
B
(–4, 5) and (4, –5)
C
(–3, 4) and (2, 0)
D
(1, –1) and (6, –5)
E
(2, –1) and (10, 9)
12

On a coordinate plane, line M N goes through (negative 4, 0) and (4, 2). Point P is at (2, negative 4).

Question illustration
A
(0, 1)
B
(0, 4)
C
(1, 0)
D
(4, 0)
13

On a coordinate plane, line A B goes through (negative 4, 0) and (2, negative 3). Point C is at (negative 2, 2).

Question illustration
A
(1, 0)
B
(1, 1)
C
(0, 2)
D
(2, 0)
14

On a coordinate plane, 2 lines are shown. Line M N goes through (negative 4, 8) and (negative 4, negative 6). Line K L goes through (negative 8, 2) and (6, 2).

Question illustration
A
The lines intersect at point K.
B
The lines are parallel.
C
The lines are perpendicular.
D
The lines do not have slopes.
15

Determine the missing information in the paragraph proof.Given: Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular. Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).Prove: The slopes of perpendicular lines are negative reciprocals.

Question illustration
A
(StartFraction d minus b Over c minus a EndFraction) (StartFraction c minus a Over negative d + b EndFraction) = negative 1
Option A
B
(StartFraction b minus a Over a + b EndFraction) (StartFraction c minus d Over negative d minus c EndFraction) = negative 1
Option B
C
(StartFraction d minus b Over c minus a EndFraction) (StartFraction c minus a Over negative d + b EndFraction) = 1
Option C
D
(StartFraction b minus a Over a + b EndFraction) (StartFraction c minus d Over negative d minus c EndFraction) = 1
Option D
16

On a coordinate plane, 4 lines are shown. Line A B goes through (negative 4, 3) and (4, 3). Line C D goes through (negative 3, 0) and (3, 2). Line F G goes through (negative 3, negative 1) and (3, negative 3). Line H J goes through (negative 1, negative 4) and (1, 2).

Question illustration
A
line AB
B
line CD
C
line FG
D
line HJ
17

Determine the missing information in the paragraph proof.Given: Line PQ contains points (w, v) and (x, z) and line P'Q' contains points (w + a, v + b) and (x + a, z + b). Lines PQ and P'Q' are parallel.Prove: Parallel lines have the same slope.

Question illustration
A
Option
Option A
B
Option
Option B
C
StartFraction v minus z + b Over x minus z + a EndFraction
Option C
D
StartFraction w minus x + a Over v minus z + b EndFraction
Option D
18

On a coordinate plane, line A B goes through (negative 2, 4) and (2, negative 8). Point C is at (6, 4).

Question illustration
A
(–6, 0)
B
(0, –6)
C
(0, 2)
D
(2, 0)
19

On a coordinate plane, a line F G goes through (negative 8, negative 8) and (8, 4). Point H is at (6, negative 6).

Question illustration
A
(–6, 10)
B
(–2, –12)
C
(0, –2)
D
(4, 2)
20

Which statements are true about these lines? Select three options.

A
The slope of line MN is .
Option A
B
The slope of line PQ is undefined.
C
The slope of line RS is .
Option C
D
Lines RS and TV are parallel.
E
Line RS is perpendicular to both line MN and line PQ.

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