This document discusses different types of transformations in geometry: reflections, translations, and rotations. Reflections involve flipping a shape across a mirror line. Translations involve sliding a shape without turning or flipping. Rotations involve turning a shape around a central point by degrees or fractions of a full turn. All of these transformations produce a new position for the shape while keeping its size, angles, and measurements the same. Tracing paper is recommended for helping to rotate shapes accurately.

1. MATHS
geometry
Transformations
By Ginny Ruadh (P7)

2. Transformations
Transformations = same shape, same size and same measurements
BUT different position.
Moving or changing shapes using strict rules.
1. Reflection,
2. Translation,
3. Rotation
After any of those transformations (turn, flip or slide),
the shape still has the same size, area, angles and line lengths.

3. 1. REFLECTION
Mirror line = FLIP
Object vs image
Object Image Object Image
The reflection of a point is the same distance from the mirror line, measured at 90% (right angels) to the line.
Your image can be double checked by folding your paper along the mirror line.
The mirror line can be vertical, horizontal of diagonal.
*It’s the same as flip horizontal on Powerpoint – if mirror line is horizontal

4. Vertical mirror line
Object
Image

5. Horizontal mirror line
Object Image

6. Vertical mirror line
t
ec
bj
O
e
ag
Im

7. 2. TRANSLATION
Translation = Sliding a shape around.
Slide = up/down + left/right
(NOT turning or flipping!)

8. Move 3 squared to the right and 5 squares down
3 blocks right
1 2 3
2
3
4
5
X
5 blocks down
On squared paper - mark each new corner point by working out their new positions.
Then join corners together

9. 3. ROTATION Rotation = TURN
Anti clockwise Turn = moving around a point (centre of rotation) Clockwise
Move = clcokwise / anti clockwise
Amount of turn = degrees/fraction (90 degrees or ¼)
Object Rotated 90° clockwise
Rotated 270° clockwise Rotated 180° clockwise
The distance from the centre Every point
to any point on the shape makes a circle
stays the same. around the center.
*Tracing paper will be your best friend for rotating objects.

10. 3. ROTATION
Anti clockwise Clockwise
Object Rotated 90° clockwise
Rotated 270° clockwise Rotated 180° clockwise
*Tracing paper will be your best friend for rotating objects.

11. 3. ROTATION
Anti clockwise Clockwise
Object Rotated 90° clockwise
Rotated 270° clockwise Rotated 180° clockwise
*Tracing paper will be your best friend for rotating objects.

12. Rotating with tracing paper
+
Trace the object, the centre (+) and the pointer (90 °/ ¼ of a rotation)
Place a pencil on the centre (pinning both pages together) and rotate the tracing paper 90° clockwise

13. Rotating with tracing paper
+
Mark the corners of the image (Leaving pressure points on original page beneath the tracing paper)
Remove the tracing paper and join the corners.

14. References
1. http://www.mathsisfun.com
2. Key Stage 2 – The Essentials of Maths (SRG)