Coordinates and trigonometry · Ages 14–15

The distance formula worksheet

Part of: Coordinate geometry

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Coordinates and trigonometry · Ages 14–15

Numsprite
numsprite.com

Name:Date:Score:／48

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

1.Find the distance between A(1, 0) and B(−5, 0): AB =
Answer:
2.In the picture, from A to B is units across and units up or down, so AB = .
Fill in each blank
Answer:
3.Find the distance between A(3, 4) and B(6, 4): AB =
Answer:
4.A(4, −4), B(−2, −6). AB =
Answer:
5.The distance between A(−2, 4) and B(−8, −4) is AB =
Answer:
6.A(1, 2), B(−5, 1). AB = (to 1 decimal place)
Answer:
7.A(6, −5), B(−6, k), with B above A and AB = 13. k =
Answer:
8.A(−5, −2), B(0, 0). AB = (to 1 decimal place)
Answer:
9.A(−3, −10), B(−11, k), with B above A and AB = 10. k =
Answer:

13.A drone flies at one height in a straight line from A(2, 8) to B(6, 4), each unit 1 m. To 1 decimal place, how far does it fly, in m?
Working:
Answer:
14.Home is at the origin O(0, 0). Four corner shops are at P(−4, −6), Q(−1, 6), R(−2, −1) and S(5, 2). Which is nearest home in a straight line?
- A. R
- B. P
- C. Q
- D. S
Choose the right answer
Working:
Answer:
15.A triangular flower bed has its corners at A(−6, −3), B(−3, −3) and C(−3, 1), each unit 1 m. How many metres of fence go all the way round it?
Working:
Answer:
16.On a map, 1 unit stands for 20 m. The post office is at A(1, 0) and the library at B(−11, 5). From A to B is units across and units up or down, a straight distance of units, which is m.
Fill in each blank
Working:
Answer:
17.A straight road runs along the x-axis. A bus stop P(k, 0) on it is to be as far from block A(0, 2) as from block B(−6, 2). k =
Working:
Answer:
18.A drone flies at one height in a straight line from A(1, 1) to B(4, 2), each unit 1 m. To 1 decimal place, how far does it fly, in m?
Working:
Answer:

Show the answers and working

The distance formula worksheet: Answers and working

1. 6
The points share a coordinate, so they are on one horizontal or vertical line: the distance is how far the other coordinate differs, 6.
2. 4, 3, 5
4 across and 3 up or down are the legs of a right triangle and AB its hypotenuse: 4² + 3² = 5.
3. 3
The points share a coordinate, so they are on one horizontal or vertical line: the distance is how far the other coordinate differs, 3.
4. 40
AB = (−2 − (4))² + (−6 − (−4))² = 36 + 4 = 40. Bracket a negative coordinate as you subtract.
5. 10
x differs by −8 − (−2) = −6, y by −4 − (4) = −8: AB = −6² + −8² = 10. A negative squared is positive.
6. 6.1
AB = (−6)² + (−1)² = 37 ≈ 6.1.
7. 0
The run is 12, so the rise = 13² − 12² = 5; B is above, so k = −5 + 5 = 0.
8. 5.4
AB = (5)² + (2)² = 29 ≈ 5.4.
9. −4
The run is 8, so the rise = 10² − 8² = 6; B is above, so k = −10 + 6 = −4.

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

13. 5.7 m
AB = (4)² + (−4)² = 32 ≈ 5.7 m.
14. A. R
Comparing the squared distances is enough: P 52, Q 37, R 5, S 29; the smallest is nearest.
15. 12 m
AB is level, 3 m; BC is upright, 4 m; AC = 3² + 4² = 5 m. The perimeter is 3 + 4 + 5 = 12 m.
16. 12, 5, 13, 260
12 across and 5 up or down: 12² + 5² = 13 units, and 13 × 20 = 260 m.
17. −3
PA² = PB²: (k − (0))² + (2)² = (k − (−6))² + (2)². Expanded, the k² terms cancel, leaving k = −3.
18. 3.2 m
AB = (3)² + (1)² = 10 ≈ 3.2 m.

Numsprite · numsprite.com/en/worksheets/coordinate-geometry/distance-formula