Coordinates and trigonometry · Ages 14–15

Using slopes worksheet

Part of: Coordinate geometry

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Coordinates and trigonometry · Ages 14–15

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A sloping path runs 17 m across and rises 3 m from start to end. Its slope = (as a fraction)
Answer in simplest form
Answer:
2.A line through A(−4, −5) and B(−2, k) has slope 31. k =
Answer:
3.A sloping path runs 31 m across and rises 3 m from start to end. Its slope = (as a fraction)
Answer in simplest form
Answer:
4.A(−6, 0), B(−12, 4), C(−15, 5). The slope of AB = and of BC = .
Fill in each blank
Answer:
5.A line through A(0, 5) and B(h, −1) has slope 34. h =
Answer:
6.A(5, 5), B(3, 7), C(1, 9). The slope of AB = and of BC = .
Fill in each blank
Answer:
7.A line through A(−6, 2) and B(h, 0) has slope −21. h =
Answer:
8.A(3, 4), B(7, −2) and C(9, k) lie on one straight line. k =
Answer:

9.A(0, 4), B(2, 0) and C(3, −1) lie on one straight line.
True or false?
Answer:
10.A line passes through A(−3, 6) and B(−2, 8). Which of these points is on it too?
- A. (−1, 10)
- B. (−3, 10)
- C. (0, 9)
- D. (−1, 6)
Choose the right answer
Answer:
11.A line passes through A(3, 6) and B(−1, 12). Which of these points is on it too?
- A. (2, 10)
- B. (−3, 9)
- C. (1, 15)
- D. (−3, 15)
Choose the right answer
Answer:
12.Ramp A's sign says "1 : 14"; ramp B runs 68 m across and rises 5 m. Which ramp is steeper?
- A. Only their lengths can tell
- B. Ramp A
- C. They are equally steep
- D. Ramp B
Choose the right answer
Answer:

13.Three lamp posts stand at A(3, 0), B(0, 2) and C(−3, 4) on a street plan. AB's slope = and BC's = ; they are equal, so the posts stand in one straight line.
Fill in each blank
Working:
Answer:
14.A straight sloping path has slope 116. Walking up it, you move 80 m across. How many metres do you rise?
Working:
Answer:
15.A ramp's slope may be at most 120. To rise 1.2 m, at least how long must it be across, in m?
Working:
Answer:
16.A cable pulled straight passes through A(3, 4) and B(5, 3) (in m). Where x = 9, the cable's y-coordinate =
Working:
Answer:
17.A ramp's slope may be at most 112. To rise 0.6 m, at least how long must it be across, in m?
Working:
Answer:
18.A straight sloping path has slope 112. Walking up it, you move 36 m across. How many metres do you rise?
Working:
Answer:

Show the answers and working

Using slopes worksheet: Answers and working

1. 317
Slope = rise ÷ distance across = 317 = 317.
2. 1
k − (−5)−2 − (−4) = 31, so k − (−5) = 31 × 2 = 6 and k = 1.
3. 331
Slope = rise ÷ distance across = 331 = 331.
4. −23, −13
AB: −23; BC: −13. Equal slopes put A, B and C in one line.
5. −8
−1 − (5)h − (0) = 34: −6 ÷ (h − (0)) = 34, so h − (0) = −8 and h = −8.
6. −1, −1
AB: −11; BC: −11. Equal slopes put A, B and C in one line.
7. −5
0 − (2)h − (−6) = −21: −2 ÷ (h − (−6)) = −21, so h − (−6) = 1 and h = −5.
8. −5
AB's slope is −32. BC's must be −32 too: k − (−2)9 − (7) = −32, so k = −5.

9. False
Compare the slopes of AB and BC: equal, they are in a line; not equal, they aren't.
10. A. (−1, 10)
From A to B each part changes x by 1 and y by 2; from B to (−1, 10) x changes by 1 and y by 2 too: the same slope, so the three are in a line.
11. D. (−3, 15)
From A to B each part changes x by −2 and y by 3; from B to (−3, 15) x changes by −2 and y by 3 too: the same slope, so the three are in a line.
12. D. Ramp B
"1 : 14" is a slope of 114; B's slope = 568. Compare 568 with 114: times 68 × 14 each side, that is 5 × 14 = 70 against 68; the larger slope is the steeper ramp.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. −23, −23
AB: 2 − (0)0 − (3) = −23; BC: 4 − (2)−3 − (0) = −23. Equal slopes through the shared B put the three in a line.
14. 5 m
Rise ÷ 80 = 116, so the rise = 116 × 80 = 5 m.
15. 24 m
1.2 ÷ run ≤ 120, so the run ≥ 1.2 × 20 = 24 m.
16. 1
AB's slope is −12. From B to x = 9: y − (3)9 − (5) = −12, so y = 1.
17. 7.2 m
0.6 ÷ run ≤ 112, so the run ≥ 0.6 × 12 = 7.2 m.
18. 3 m
Rise ÷ 36 = 112, so the rise = 112 × 36 = 3 m.

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