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′.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- translation
- a slide with no turning or flipping
- reflection
- a flip in a mirror line
- rotation
- a turn about a centre point
- image
- where a shape or point ends up after a transformation
Worked examples
A is at (2, 3). Triangle ABC is translated 4 units right and 2 units up. Where is A′?
- 1.Right 4: 2 + 4 = 6.
- 2.Up 2: 3 + 2 = 5.
= (6, 5)
B is at (3, 4). Triangle ABC is reflected in the vertical mirror line through 5. Where is B′?
- 1.B is 2 units left of the line.
- 2.Go 2 units past it: 5 + 2 = 7. The up number stays 4.
= (7, 4)
C is at (6, 5). Triangle ABC is rotated 90° clockwise about P (4, 5). Where is C′?
- 1.From P, C is 2 right.
- 2.A clockwise quarter turn makes 'right' into 'down': 2 down from P.
= (4, 3)
For parents
Method: Follow one corner at a time and count grid jumps, writing coordinates (across, up).
What to say: Where is the corner now? Which way does it move, and how far?
Common mistakes:
- Makes only the first move of a two-part translation and forgets the second.
- Applies the left–right move to the up number and the up–down move to the across number.
- Counts the starting grid line as step 1, so each move lands one unit short.
- Moves the wrong way left or right (left–right confusion).
- Moves the wrong way up or down: treats 'down' as making the second number bigger, as if counting rows down a page.
- Finds the image point but writes its coordinates the wrong way round (up, across).
- Slides the shape across the mirror line without flipping it, as if a reflection were a translation.
- Counts the mirror line itself as one step when measuring beyond it, so the image lands one unit too close.
- Turns anticlockwise instead of clockwise (or the reverse).
- Confuses a quarter turn (90°) with a half turn (180°).
- For a quarter turn, swaps the across and up distances from the centre but keeps both directions, which reflects rather than rotates.
- For a half turn, flips the point over a line through the centre instead of turning it.