First steps in coordinates · Ages 12–13
Distance along a horizontal or vertical line
Larger minus smaller: 3 − (−4) = 7.
How to do it
Method
Larger minus smaller: 3 − (−4) = 7
(−4, 2) and (3, 2): 3 − (−4) = 7
Another way
Add the two parts
4 + 3 = 7
In full
Two points on one horizontal line (the same y-coordinate) are as far apart as their x-coordinates differ; on one vertical line (the same x), look at how the y-coordinates differ. Take the smaller from the larger: (−4, 2) and (3, 2) are 3 − (−4) = 7 apart. Or add the two parts: (−4, 2) is 4 from the y-axis and (3, 2) is 3, so 4 + 3 = 7. Only on the same side of an axis do you subtract: (−6, 1) and (−2, 1) are 6 − 2 = 4 apart. A distance is never negative; counting squares works too, counting the sides of squares, not the points.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The distance between P(1, 8) and Q(1, −2) is units.
Show the answer and working
Answer: 10
They share an x-coordinate, so they are on one vertical line, and 8 and −2 differ by 10.
Example 2
The points (4, −5) and (−7, −5) are 3 units apart.
True or false?
Show the answer and working
Answer: False
The points are either side of the y-axis, so the distance is the two parts added: 11 units, not their difference.
Example 3
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?
Show the answer and working
Answer: 18
A(−5, 5) to B(3, 5) is horizontal, across the y-axis, so add the two parts: 8; B to C(3, −5) is vertical, across the x-axis: 10. In all 8 + 10 = 18 units.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The distance between A(−3, 0) and B(1, 0) is units.
Answer:
2.How many units apart are A(−2, 9) and B(5, 9)?
- A. 3
- B. 7
- C. 8
- D. 5
Choose the right answer
Answer:
3.The points (−9, −1) and (4, −1) are 5 units apart.
True or false?
Answer:
4.B is to the left of A(0, −2), AB = 6 units and AB is horizontal. B is (, ).
Fill in each blank
Answer:
5.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:
All the answers
- 1. 4
- 2. B. 7
- 3. False
- 4. −6, −2
- 5. 15
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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