Geometry, Year 8: translating, rotating and enlarging

(6, −2)

提示Right changes the first number; down changes the second.

为什么2 + 4 = 6 and 3 − 5 = −2. Every point of a shape moves by the same amount in a translation.

3 left and 4 up

提示Subtract old from new, one coordinate at a time.

为什么The x-coordinate goes from 1 to −2, a change of −3, which is 3 left. The y-coordinate goes from 1 to 5, a change of +4, which is 4 up.

Only its position

提示A translation is a slide, nothing more.

为什么The shape is not turned, flipped or resized. Every side stays the same length and points the same way.

Yes — same size and same shape

提示Sliding does not stretch or squash anything.

为什么Congruent means identical in size and shape. Translations, rotations and reflections all give congruent images; enlargements do not.

(−3, −1)

提示A half turn takes every point to the opposite side of the centre.

为什么A half turn about the origin reverses the sign of both coordinates. The image is as far beyond the centre as the point was before it.

(0, 2)

提示Picture the hand of a clock moving backwards by a quarter turn.

为什么The point starts 2 units to the right of the origin. A quarter turn anticlockwise swings it round to 2 units directly above.

The centre of rotation

提示It is the one point that does not move.

为什么A given angle about different centres sends a shape to different places, so without this third piece of information the description is incomplete.

Tracing paper

提示You can see through it and pin it down with a pencil point.

为什么Trace the shape, hold the pencil point on the centre and turn the sheet through the angle. The tracing should land exactly on the image.

9 cm, 12 cm and 15 cm

提示Every length is multiplied by the same number.

为什么3 × 3 = 9, 4 × 3 = 12 and 5 × 3 = 15. The scale factor multiplies every length in the shape.

They stay the same

提示The shape keeps its look; only the lengths grow.

为什么An enlargement changes size but not shape. If the angles changed, the image would be a different shape altogether.

6 squares right and 3 up

提示Stretch the journey out from the centre by the scale factor.

为什么Each distance from the centre is multiplied by 3: 2 becomes 6 and 1 becomes 3. The image lies on the straight line from the centre through A.

3

提示Divide the new length by the old one.

为什么12 ÷ 4 = 3. The scale factor is always image length ÷ object length for a pair of matching sides.