Point A(1, 7) is □ units from the y-axis and □ units from the x-axis. Fill in each blank

1, 7. The distance from the y-axis runs across, so it comes from x = 1: 1 unit. From the x-axis it runs up or down, from y = 7: 7 units. A distance is never negative.

First steps in coordinates · Ages 12–13

Reading and plotting points

Across first, then up or down: (x, y).

How to do it

Method

Across first, then up or down: (x, y)

(−3, 2): 3 left, 2 up

Another way

Look to the axes

Down to the x-axis for x, across to the y-axis for y

In full

A coordinate plane is two number lines at right angles: the x-axis across, the y-axis up, meeting at the origin O(0, 0). A point is written (x, y): the x-coordinate (left or right) first, then the y-coordinate (up or down); right and up are positive, left and down negative. To read a point, look straight down or up to the x-axis for x, and straight across to the y-axis for y. To plot one, start at the origin, go across to x, then up or down to y. (−3, 2) is 3 left and 2 up; (2, −3) is another point, so x and y can't be swapped.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
Write the coordinates of A and B: A(, ), B(, ).
Fill in each blank
Show the answer and working
Answer: −4, −2, 5, −5
From A, the x-axis reads −4 and the y-axis −2, so A(−4, −2); likewise B(5, −5). x first, then y.
Example 2
Point A(1, 7) is units from the y-axis and units from the x-axis.
Fill in each blank
Show the answer and working
Answer: 1, 7
The distance from the y-axis runs across, so it comes from x = 1: 1 unit. From the x-axis it runs up or down, from y = 7: 7 units. A distance is never negative.
Example 3
Which point is at (3, −4)?
- A. C
- B. A
- C. B
- D. D
Choose the right answer
Show the answer and working
Answer: C. B
From the origin go across to 3, then up or down to −4: that point is the one. The other three swap x and y or lose a sign.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.What are the coordinates of point P?
- A. (−3, −4)
- B. (−3, 4)
- C. (3, 4)
- D. (4, −3)
Choose the right answer
Answer:
2.Write the coordinates of A and B: A(, ), B(, ).
Fill in each blank
Answer:
3.Point A(−3, −2) is units from the y-axis and units from the x-axis.
Fill in each blank
Answer:
4.Which point is at (−5, 6)?
- A. A
- B. C
- C. D
- D. B
Choose the right answer
Answer:
5.Which picture plots A(3, 1) and B(3, 5) correctly?
- A
- B
- C
- D
Choose the right picture
Answer:

All the answers

1. B. (−3, 4)
2. −2, −6, 1, 5
3. 3, 2
4. C. D
5. A

Free worksheet: Reading and plotting pointsWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

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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