Geometry, Year 8: translating, rotating and enlarging：全部卡片
整套按顺序列出——孩子看到之前，您可以先通读一遍。
- Point A (2, 3) is translated 4 right and 5 down. What are the coordinates of its image?
(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.
- 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
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.
- After a translation, which of these changes: the shape's size, the way it faces, or its position?
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.
- Is a shape congruent to its image after a translation?
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.
- Point (3, 1) is rotated 180° about the origin. Where does it land?
(−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.
- Point (2, 0) is rotated 90° anticlockwise about the origin. Where does it land?
(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.
- To describe a rotation fully, you need the angle, the direction and what else?
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.
- Which piece of equipment lets you check a rotation by turning a copy of the shape about the centre?
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.
- 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
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.
- A shape is enlarged by scale factor 2. What happens to its angles?
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.
- 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
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.
- A side of 4 cm becomes 12 cm after an enlargement. What is the scale factor? (number only)
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.
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