Coordinates and trigonometry · Ages 14–15
Slopes of parallel and perpendicular lines worksheet
Part of: Coordinate geometry
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Slopes of parallel and perpendicular lines worksheet
Coordinates and trigonometry · Ages 14–15
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.Line L₁ has slope 54, and line L₂ is perpendicular to L₁. L₂'s slope =
Answer in simplest form
Answer:
2.Line L₁ passes through A(4, −1) and B(−4, 2), and line L₂ is parallel to L₁. L₂'s slope =
Answer in simplest form
Answer:
3.Line L₁ has slope −43, and line L₂ is perpendicular to L₁. L₂'s slope =
Answer in simplest form
Answer:
4.A(−6, 6), B(−12, 12), C(−3, 5), D(3, k), and AB ∥ CD. k =
Answer:
5.A(2, 5), B(6, 11), C(2, 2), D(6, k), and AB ∥ CD. k =
Answer:
6.L₁ passes through A(1, −5) and B(0, −3), L₂ through C(−2, −5) and D(2, −7). L₁'s slope = , L₂'s slope = , and their product = .
Fill in each blank
Answer:
7.A(2, −2), B(−4, −4), C(−3, 3), D(−5, k), and AB ⊥ CD. k =
Answer:
8.L₁ passes through A(6, −5) and B(3, −7), L₂ through C(−1, −4) and D(3, −10). L₁'s slope = , L₂'s slope = , and their product = .
Fill in each blank
Answer:
9.A(5, 4), B(1, 0), C(6, −4), D(2, k), and AB ⊥ CD. k =
Answer:
Part B: Choose, or true or false (2 marks each)
10.Lines of slopes −53 and −35 are perpendicular.
True or false?
Answer:
11.What is the slope of a line perpendicular to one of slope −12?
- A. 21
- B. −12
- C. 12
- D. −21
Choose the right answer
Answer:
12.What is the slope of a line perpendicular to one of slope 12?
- A. −12
- B. 21
- C. −21
- D. 12
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.A straight road passes through A(4, −4) and B(8, 2). A footpath from C(−3, 0) meets the road at right angles and passes through D(−6, k). k =
Working:
Answer:
14.On a plan, road L₁ passes through A(0, −6) and B(3, −8), and road L₂ through C(6, 5) and D(10, 11). L₁'s slope = and L₂'s = ; they multiply to −1, so the roads are perpendicular.
Fill in each blank
Working:
Answer:
15.In a garden, fence AB runs from A(3, 6) to B(9, 2). Another fence CD is parallel to AB, with C(2, −1) and D(h, −3). h =
Working:
Answer:
16.On a plan, corridor AB runs from A(6, −5) to B(7, −6) and corridor CD from C(−4, 1) to D(−4, 0). The corridors are perpendicular.
True or false?
Working:
Answer:
17.On a plan, road L₁ passes through A(5, −3) and B(8, −4), and road L₂ through C(−2, −1) and D(−1, 2). L₁'s slope = and L₂'s = ; they multiply to −1, so the roads are perpendicular.
Fill in each blank
Working:
Answer:
18.On a plan, corridor AB runs from A(−5, 1) to B(−6, 0) and corridor CD from C(5, 3) to D(4, 5). The corridors are perpendicular.
True or false?
Working:
Answer:
Show the answers and working
Slopes of parallel and perpendicular lines worksheet: Answers and working
Part A: Working out and filling in
1. −45
54 × m₂ = −1, so m₂ = −45: turn 54 over and change its sign.
2. −38
Parallel lines have equal slopes: L₁'s is 3−8 = −38, so L₂'s is −38.
3. 34
−43 × m₂ = −1, so m₂ = 34: turn −43 over and change its sign.
4. −1
Parallel means equal slopes: AB's is −11, so k − (5)3 − (−3) = −11 and k = −1.
5. 8
Parallel means equal slopes: AB's is 32, so k − (2)6 − (2) = 32 and k = 8.
6. −2, −12, 1
L₁: −21; L₂: −12; the product 11. Only a product of −1 makes them perpendicular.
7. 9
AB's slope is 13, so CD's is −31: k − (3)−5 − (−3) = −31, so k = 9.
8. 23, −32, −1
L₁: 23; L₂: −32; the product −11. Only a product of −1 makes them perpendicular.
9. 0
AB's slope is 11, so CD's is −11: k − (−4)2 − (6) = −11, so k = 0.
Part B: Choose, or true or false
10. False
Perpendicular means the slopes multiply to −1: work out −53 × −35 and see whether it is −1.
11. A. 21
Perpendicular slopes multiply to −1: −12 × m = −1, so m is −12 turned over with its sign changed.
12. C. −21
Perpendicular slopes multiply to −1: 12 × m = −1, so m is 12 turned over with its sign changed.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 2
The road's slope is 32, the footpath's −23: k − (0)−6 − (−3) = −23, so k = 2.
14. −23, 32
L₁: −23; L₂: 32; −23 × (32) = −1.
15. 5
Parallel means equal slopes: −3 − (−1)h − (2) = −23, so h − (2) = (−3 − (−1)) ÷ −23 and h = 5.
16. False
Find both corridors' slopes and see whether they multiply to −1 (if one is upright, see whether the other is level).
17. −13, 3
L₁: −13; L₂: 31; −13 × (31) = −1.
18. False
Find both corridors' slopes and see whether they multiply to −1 (if one is upright, see whether the other is level).
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