Shape and space · Ages 9–10

Coordinates and moving shapes worksheet

Covers: Grid references, Coordinates (x, y), Plotting shapes, Translations, Reflections, Rotations, Congruent shapes

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Shape and space · Ages 9–10

Numsprite
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Name:Date:Score:／48

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

1.The 🐵 is in B3 and the 🍌 is in E5. The 🐵 moves one square at a time, left, right, up or down. What is the fewest squares it must move to reach the 🍌?
Answer:
2.Each square on the paper is 1 cm wide. What is the perimeter of rectangle ABCD in cm?
Answer:
3.Square ABCD has A at (4, 3) and B at (8, 3), with C and D above AB. C is at (, ).
Fill in each blank
Answer:
4.Shape Q is shape P after a translation. P moved squares right and squares up.
Fill in each blank
Answer:
5.The point (5, 3) moves 3 squares right and 3 squares up. Its new position is (, ).
Fill in each blank
Answer:
6.Triangle ABC turns 90° clockwise about corner A. What is the x-coordinate of C′, C's new position?
Answer:

7.Which square is the 📎 in?
- A. B5
- B. B2
- C. D5
- D. D2
Choose the right answer
Answer:
8.What are the coordinates of point A?
- A. (2, 6)
- B. (6, 2)
- C. (5, 1)
- D. (1, 5)
Choose the right answer
Answer:
9.Point A is at (6, 8).
True or false?
Answer:
10.The green slanting line is the mirror line, through (0, 0), (1, 1), (2, 2), …. Which picture shows the orange triangle's image (blue) correctly?
- A
- B
- C
- D
Choose the right picture
Answer:
11.The green line is a mirror line. Shape Q is the reflection of shape P.
True or false?
Answer:
12.How is shape Q made from shape P?
- A. No move of P makes it (not congruent)
- B. A rotation (turn)
- C. A reflection (flip)
- D. A translation (slide)
Choose the right answer
Answer:

13.A car park's spaces are named with columns A to F and rows 1 to 8, one space to a square. How many spaces are there?
Working:
Answer:
14.In a video game, Ming's character is at (7, 0). Ming presses “↑” 3 times and “←” 2 times, one square a press. The character is now at (, ).
Fill in each blank
Working:
Answer:
15.On a map each square's side stands for 2 m. A rectangular lawn has opposite corners at (4, 0) and (6, 5). How many metres of fence go all the way round it?
Working:
Answer:
16.A crane at the container port slides a container: its bottom left corner moves from (3, 3) to (9, 0). The container moved squares right and squares down.
Fill in each blank
Working:
Answer:
17.On a floor plan, a door's hinge is at (3, 2). Shut, the door's other end is at (6, 2). The door swings 90° anticlockwise about the hinge; its other end is now at (, ).
Fill in each blank
Working:
Answer:
18.Ka-lok lays 2 congruent rectangular cards side by side, long side against long side, to make one big rectangle. Each card is 9 cm long and 5 cm wide. What is the big rectangle's perimeter in cm?
Working:
Answer:

Show the answers and working

Coordinates and moving shapes worksheet: Answers and working

1. 5 squares
Count the two parts apart: how many squares across from B to E, and how many up or down from row 3 to row 5?
B to E is 3 squares across; row 3 to row 5 is 2 more: 5 in all.
2. 10 cm
Count the squares along AB and along BC. A rectangle's perimeter is two lengths and two widths.
AB = 8 − 4 = 4 cm and BC = 1 − 0 = 1 cm, so the perimeter is 2 × (4 + 1) = 10 cm.
3. 8, 7
Work out how long AB is from A's and B's x first. A square's upright side is just as long.
AB is 8 − 4 = 4 squares; a square's sides are equal, so C is 4 straight above B: (8, 7).
4. 3, 1
Pick one corner, say the right angle, find it on P and on Q, then count how far it moved.
Follow one corner: the right angle moves from (0, 1) to (3, 2), 3 right and 1 up.
5. 8, 6
Right adds to x, up adds to y. Start from (5, 3).
Right adds 3 to x: 8. Up adds 3 to y: 6.
6. 6
A stays put. AC points 3 up; turning 90° clockwise, which way does “up” become?
AC points 3 up; clockwise 90° turns “up” into “right”: C′ is 3 right of A, so x is 3 + 3 = 6.

7. A. B5
Find the 📎: look down to see which letter's column it is in, then which row.
Look down from the 📎 to the letter and across to the number: the letter first, then the number.
8. D. (1, 5)
Look down from A to the x-axis and across to the y-axis. Count from 0 at the origin, and write x first.
Down from A to the x-axis reads 1; across to the y-axis reads 5: (1, 5).
9. True
Read x down from A and y across from it, then compare with (6, 8) one number at a time, in order.
Down from A is 6 on the x-axis, across is 8 on the y-axis: A is (6, 8).
10. B
In this slanting mirror (x, y) goes to (y, x). Find where the right angle (6, 1) goes first.
In this slanting mirror the image of (x, y) is (y, x): the right angle (6, 1) goes to (1, 6).
11. True
See how far P's right angle is from the mirror. Is Q's just as far on the other side, and is Q flipped?
The reflection has each corner of P flipped to the other side of the mirror, the same distance from it.
12. A. No move of P makes it (not congruent)
Count the squares along the sides first to see if Q is P's size; then look at which way Q faces.
Compare the size first (the squares along the sides), then the way it faces: the same way is a slide, flipped is a reflection, turned round is a rotation.

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

13. 48 spaces
First count how many columns A to F makes; each column has 8 spaces.
A to F is 6 columns of 8: 6 × 8 = 48.
14. 5, 3
↑ changes y and ← changes x. Going left, does x get bigger or smaller?
← is left, so x goes down by 2: 5. ↑ is up, so y goes up by 3: 3.
15. 28 m
Use the two corners to find how many squares long and wide it is: 6 − 4 and 5 − 0.
Once you have the perimeter in squares, remember each square's side stands for 2 m.
6 − 4 = 2 squares long and 5 − 0 = 5 wide: the perimeter is 2 × (2 + 5) × 2 = 28 m.
16. 6, 3
Compare the two x's, 3 and 9; then the two y's, 3 and 0.
x goes from 3 to 9: 6 right. y goes from 3 to 0: 3 down.
17. 3, 5
The hinge stays put; the door is 3 squares long and points right. A quarter turn anticlockwise turns “right” into which way?
The door is 3 squares long and pointed right; turned 90° anticlockwise it points up: (3, 5).
18. 38 cm
Work out the big rectangle's length and width first: with the long sides together, which way doubles?
The big rectangle is 9 long and 5 + 5 = 10 wide: perimeter 2 × (9 + 10) = 38.

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