Geometry, Year 8: translating, rotating and enlarging

(6, −2)

HintRight changes the first number; down changes the second.

The why2 + 4 = 6 and 3 − 5 = −2. Every point of a shape moves by the same amount in a translation.

3 left and 4 up

HintSubtract old from new, one coordinate at a time.

The whyThe 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

HintA translation is a slide, nothing more.

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

Yes — same size and same shape

HintSliding does not stretch or squash anything.

The whyCongruent means identical in size and shape. Translations, rotations and reflections all give congruent images; enlargements do not.

(−3, −1)

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

The whyA 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)

HintPicture the hand of a clock moving backwards by a quarter turn.

The whyThe 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

HintIt is the one point that does not move.

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

Tracing paper

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

The whyTrace 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

HintEvery length is multiplied by the same number.

The why3 × 3 = 9, 4 × 3 = 12 and 5 × 3 = 15. The scale factor multiplies every length in the shape.

They stay the same

HintThe shape keeps its look; only the lengths grow.

The whyAn enlargement changes size but not shape. If the angles changed, the image would be a different shape altogether.

6 squares right and 3 up

HintStretch the journey out from the centre by the scale factor.

The whyEach 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

HintDivide the new length by the old one.

The why12 ÷ 4 = 3. The scale factor is always image length ÷ object length for a pair of matching sides.