geometry · Year 5 · AC9M5SP03

Translate, reflect and rotate

A transformation moves a shape. To find where a corner goes, follow that one corner. Translation slides the shape: add for right and up, subtract for left and down. Reflection flips it in a mirror line: count how far the corner is from the line, then go the same distance on the other side. Rotation turns it about a centre point P: note how far the corner is from P across and up, then turn those moves. For a quarter turn clockwise, 'right' becomes 'down' and 'up' becomes 'right'. For a half turn, both moves reverse. The image of A is written A′.

Sample questions

Triangle ABC is translated 2 units up. What are the coordinates of A′, the image of A?

01122334455667788991010ABC
  1. A is at (7, 4).
  2. 2 units up changes the up number: 4 + 2 = 6.
  3. A′ is at (7, 6).

Answer: (7, 6)

Triangle ABC is translated 3 units left. What are the coordinates of B′, the image of B?

01122334455667788991010ABC
  1. B is at (3, 10).
  2. 3 units left changes the across number: 3 − 3 = 0.
  3. B′ is at (0, 10).

Answer: (0, 10)

Triangle ABC is translated 5 units right. What are the coordinates of A′, the image of A?

01122334455667788991010ABC
  1. A is at (5, 3).
  2. 5 units right changes the across number: 5 + 5 = 10.
  3. A′ is at (10, 3).

Answer: (10, 3)

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