Every card in Geometry, Year 8: translating, rotating and enlarging
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← Back to Geometry, Year 8: translating, rotating and enlarging
- Point A (2, 3) is translated 4 right and 5 down. What are the coordinates of its image?
(6, −2)
HintRight changes the first number; down changes the second.
Why2 + 4 = 6 and 3 − 5 = −2. Every point of a shape moves by the same amount in a translation.
- Triangle P has a vertex at (1, 1). After a translation, the matching vertex is at (−2, 5). Describe the translation.
3 left and 4 up
HintSubtract old from new, one coordinate at a time.
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.
- After a translation, which of these changes: the shape's size, the way it faces, or its position?
Only its position
HintA translation is a slide, nothing more.
WhyThe shape is not turned, flipped or resized. Every side stays the same length and points the same way.
- Is a shape congruent to its image after a translation?
Yes — same size and same shape
HintSliding does not stretch or squash anything.
WhyCongruent means identical in size and shape. Translations, rotations and reflections all give congruent images; enlargements do not.
- Point (3, 1) is rotated 180° about the origin. Where does it land?
(−3, −1)
HintA half turn takes every point to the opposite side of the centre.
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.
- Point (2, 0) is rotated 90° anticlockwise about the origin. Where does it land?
(0, 2)
HintPicture the hand of a clock moving backwards by a quarter turn.
WhyThe point starts 2 units to the right of the origin. A quarter turn anticlockwise swings it round to 2 units directly above.
- To describe a rotation fully, you need the angle, the direction and what else?
The centre of rotation
HintIt is the one point that does not move.
WhyA given angle about different centres sends a shape to different places, so without this third piece of information the description is incomplete.
- Which piece of equipment lets you check a rotation by turning a copy of the shape about the centre?
Tracing paper
HintYou can see through it and pin it down with a pencil point.
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.
- A triangle with sides 3 cm, 4 cm and 5 cm is enlarged by scale factor 3. What are the new side lengths?
9 cm, 12 cm and 15 cm
HintEvery length is multiplied by the same number.
Why3 × 3 = 9, 4 × 3 = 12 and 5 × 3 = 15. The scale factor multiplies every length in the shape.
- A shape is enlarged by scale factor 2. What happens to its angles?
They stay the same
HintThe shape keeps its look; only the lengths grow.
WhyAn enlargement changes size but not shape. If the angles changed, the image would be a different shape altogether.
- Point A is 2 squares right and 1 up from the centre of enlargement. Under scale factor 3, where is its image, measured from the centre?
6 squares right and 3 up
HintStretch the journey out from the centre by the scale factor.
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.
- A side of 4 cm becomes 12 cm after an enlargement. What is the scale factor? (number only)
3
HintDivide the new length by the old one.
Why12 ÷ 4 = 3. The scale factor is always image length ÷ object length for a pair of matching sides.
1★ KS3-MATH-GEO-0066
2★ KS3-MATH-GEO-0067
3★ KS3-MATH-GEO-0068
4★ KS3-MATH-GEO-0069
5★ KS3-MATH-GEO-0070
6★ KS3-MATH-GEO-0071
7★ KS3-MATH-GEO-0072
8★ KS3-MATH-GEO-0073
9★ KS3-MATH-GEO-0074
10★ KS3-MATH-GEO-0075
11★ KS3-MATH-GEO-0076
12★ KS3-MATH-GEO-0077
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