Coordinates and trigonometry · Ages 12–13

Reading and plotting points worksheet

Part of: First steps in coordinates

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Coordinates and trigonometry · Ages 12–13

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

1.Write the coordinates of A and B: A(, ), B(, ).
Fill in each blank
Answer:
2.Point A(3, −1) is units from the y-axis and units from the x-axis.
Fill in each blank
Answer:
3.Point A(−4, 6) is units from the y-axis and units from the x-axis.
Fill in each blank
Answer:
4.Rectangle ABCD has its sides parallel to the axes, with A(−3, −5), B(−4, −5) and C(−4, 3). D is (, ).
Fill in each blank
Answer:

5.Going 2 units left from the origin, then 1 unit up, reaches the point (1, −2).
True or false?
Answer:
6.What are the coordinates of point P?
- A. (2, 4)
- B. (−2, −4)
- C. (2, −4)
- D. (−4, 2)
Choose the right answer
Answer:
7.Going 4 units left from the origin, then 2 units up, reaches the point (−4, 2).
True or false?
Answer:
8.Which point is at (−3, −6)?
- A. B
- B. C
- C. A
- D. D
Choose the right answer
Answer:
9.Which picture plots A(5, 1) and B(−2, 3) correctly?
- A
- B
- C
- D
Choose the right picture
Answer:
10.Which point is at (3, −5)?
- A. A
- B. C
- C. B
- D. D
Choose the right answer
Answer:
11.Joining A(−3, 5), B(4, 5) and C(−4, 2) in turn: which picture is right?
- A
- B
- C
- D
Choose the right picture
Answer:
12.Joining A(1, 2), B(−4, 1) and C(5, 3) in turn: which picture is right?
- A
- B
- C
- D
Choose the right picture
Answer:

13.A robot starts at (−4, −4), goes 4 units right, then 4 units down, then 9 units left. What is the x-coordinate where it stops?
Working:
Answer:
14.A road runs straight up and down through the phone box at P(−4, 1). Which of these places is on the road too?
- A. (4, 1)
- B. (−4, 5)
- C. (5, 1)
- D. (1, −4)
Choose the right answer
Working:
Answer:
15.An ant starts at the origin, crawls 4 units right, then 6 units down. Which point does it reach?
- A. (4, 6)
- B. (−6, 4)
- C. (−4, −6)
- D. (4, −6)
Choose the right answer
Working:
Answer:
16.Square ABCD has sides parallel to the axes, A(−6, 4) and B(−3, 4), with C and D below AB. What is C's y-coordinate?
Working:
Answer:
17.On a treasure map, the treasure T is on the same vertical line as A(−6, 4) and the same horizontal line as B(−3, 3). T is at (, ).
Fill in each blank
Working:
Answer:
18.A map has the square at the origin O, the x-axis pointing east and the y-axis north. P is the post office, Q the park. The post office is at (, ), the park at (, ).
Fill in each blank
Working:
Answer:

Show the answers and working

Reading and plotting points worksheet: Answers and working

1. −2, 3, 4, 5
From A, the x-axis reads −2 and the y-axis 3, so A(−2, 3); likewise B(4, 5). x first, then y.
2. 3, 1
The distance from the y-axis runs across, so it comes from x = 3: 3 units. From the x-axis it runs up or down, from y = −1: 1 unit. A distance is never negative.
3. 4, 6
The distance from the y-axis runs across, so it comes from x = −4: 4 units. From the x-axis it runs up or down, from y = 6: 6 units. A distance is never negative.
4. −3, 3
AB is horizontal and BC vertical, so D is straight above or below A (x = −3) and level with C (y = 3).

5. False
Left is negative and up positive, and left or right is written first: it reaches (−2, 1).
6. C. (2, −4)
Straight above or below P the x-axis reads 2; straight across, the y-axis reads −4: P(2, −4).
7. True
Left is negative and up positive, and left or right is written first: it reaches (−4, 2).
8. C. A
From the origin go across to −3, then up or down to −6: that point is the one. The other three swap x and y or lose a sign.
9. D
A: from the origin go across to 5, then up or down to 1; B: across to −2, then to 3.
10. D. D
From the origin go across to 3, then up or down to −5: that point is the one. The other three swap x and y or lose a sign.
11. B
Plot one point at a time, across to x and then up or down to y, and join them in turn.
12. A
Plot one point at a time, across to x and then up or down to y, and join them in turn.

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

13. −9
Only left and right change x: −4 + 4 − 9 = −9. Going down leaves x alone.
14. B. (−4, 5)
Every point on a vertical line has the same x: look for x = −4.
15. D. (4, −6)
4 right: x = 4; 6 down: y = −6. It reaches (4, −6).
16. 1
AB is the gap between −6 and −3, so 3, the square's side; C is 3 straight below B: 4 − 3 = 1.
17. −6, 3
On one vertical line, x is the same: −6; on one horizontal line, y is the same: 3.
18. −4, −2, 1, 6
From P, read x off the x-axis and y off the y-axis: P(−4, −2); likewise Q(1, 6). West and south of the square are negative.

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