Coordinates and trigonometry · Ages 12–13

Distance along a horizontal or vertical line worksheet

Part of: First steps in coordinates

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Coordinates and trigonometry · Ages 12–13

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

1.The distance between A(−2, 5) and B(−3, 5) is units.
Answer:
2.The distance between P(9, −4) and Q(9, 6) is units.
Answer:
3.The distance between A and B in the picture is units.
Answer:
4.A(−9, 3) and B(7, 3): A is units from the y-axis, B is units from it, so AB = units.
Fill in each blank
Answer:
5.A(2, −4) is straight above B, and AB = 8 units. B's y-coordinate is .
Answer:
6.A(9, 9) is straight above B, and AB = 2 units. B's y-coordinate is .
Answer:
7.B is to the left of A(−2, −3), AB = 3 units and AB is horizontal. B is (, ).
Fill in each blank
Answer:
8.In the picture, an ant crawls in a straight line from A to B, then straight on to C. How many units does it crawl in all?
Answer:

13.In square ABCD, A(−5, 2) and B(3, 2), with C straight below B. What is C's y-coordinate?
Working:
Answer:
14.With ground level as the x-axis and units of metres, a drone at (−3, 27) drops 35 m straight down into a valley. What is its y-coordinate now?
Working:
Answer:
15.Rectangle ABCD has corners A(−6, 3), B(7, 3), C(7, −4) and D(−6, −4). AB = , BC = , area = square units.
Fill in each blank
Working:
Answer:
16.A sea chart has the pier at the origin. Which pair of buoys is 10 units apart?
- A. (4, 0) and (6, 0)
- B. (−4, 0) and (6, 0)
- C. (−4, 0) and (0, 6)
- D. (−4, 6) and (−4, −3)
Choose the right answer
Working:
Answer:
17.With the pier at the origin and units of km, a fishing boat is at (−2, 13) and a buoy at (−2, −8). How far apart are they?
Working:
Answer:
18.A(2, 1) and B(2, −3) are on one vertical line. AB = units; C is 5 units straight below B, and AC = units.
Fill in each blank
Working:
Answer:

Show the answers and working

Distance along a horizontal or vertical line worksheet: Answers and working

1. 1
They share a y-coordinate, so they are on one horizontal line: the distance is how far apart the x-coordinates are, and −2 and −3 differ by 1.
2. 10
They share an x-coordinate, so they are on one vertical line, and −4 and 6 differ by 10.
3. 1
A(−4, 5) and B(−3, 5) share one coordinate, so the distance is how far apart the other is: 1 unit.
4. 9, 7, 16
The points are either side of the y-axis, so add the two parts: 9 + 7 = 16.
5. −12
B is 8 units below A: its y-coordinate is −4 − 8 = −12.
6. 7
B is 2 units below A: its y-coordinate is 9 − 2 = 7.
7. −5, −3
AB is horizontal, so y stays −3; B is to the left, so take 3 from x: −2 − 3 = −5.
8. 10
A(3, −3) to B(−2, −3) is horizontal, across the y-axis, so add the two parts: 5; B to C(−2, 2) is vertical, across the x-axis: 5. In all 5 + 5 = 10 units.

9. B. 10
A is 3 left of the y-axis and B 7 right: 3 + 7 = 10, which is 7 − (−3) = 10.
10. D. 4
A is 1 left of the y-axis and B 3 right: 1 + 3 = 4, which is 3 − (−1) = 4.
11. True
The points are either side of the y-axis, so the distance is the two parts added: 12 units, not their difference.
12. B. 1
The points share one coordinate; the other is −8 and −7, on the same side of the axis, so larger minus smaller: (−7) − (−8) = 8 − 7 = 1.

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

13. −6
The side AB = 5 + 3 = 8; C is 8 below B: 2 − 8 = −6.
14. −8
Straight down: x stays and y loses 35, 27 − 35 = −8. Below ground level it is negative.
15. 13, 7, 91
AB crosses the y-axis: 6 + 7 = 13; BC crosses the x-axis: 3 + 4 = 7; area = 13 × 7 = 91.
16. B. (−4, 0) and (6, 0)
(−4, 0) and (6, 0) are on one horizontal line, either side of the y-axis: 4 + 6 = 10.
17. 21 km
Same x, so one vertical line, either side of the x-axis: 13 + 8 = 21 km.
18. 4, 9
A is 1 above the x-axis and B 3 below: AB = 4; C is 5 lower still: AC = 4 + 5 = 9.

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