Grade 10 core mathematics – Similarity and Enlargement Quiz
1. Which of the following best describes similar shapes?
Similar shapes have the same shape so corresponding angles are equal and corresponding side lengths are in the same ratio (proportional).
2. Triangle PQR has sides 3 cm, 4 cm and 5 cm. A triangle similar to PQR has corresponding sides 6 cm, 8 cm and 10 cm. What is the scale factor of enlargement?
Each side of the image is twice the original (6/3 = 8/4 = 10/5 = 2), so the scale factor is 2.
3. A triangle is enlarged by a scale factor of 3. If the original perimeter is 18 cm, what is the perimeter of the enlarged triangle?
Perimeter scales by the same linear scale factor. 18 cm × 3 = 54 cm.
4. If a figure is enlarged by a scale factor of 4, by what factor does its area increase?
Area scales by the square of the linear scale factor: 4^2 = 16, so area becomes 16 times larger.
5. The area of a shape becomes 9 times larger after enlargement. What is the linear scale factor?
If area scale = k^2 = 9, then k = sqrt(9) = 3. The linear scale factor is 3.
6. Point A(2, -3) is enlarged from the origin by a scale factor of 4. What are the coordinates of the image A'?
Enlargement from the origin multiplies both coordinates by the scale factor: (2×4, -3×4) = (8, -12).
7. An enlargement has centre (1,1) and scale factor 2. The point (3,4) is mapped to which point?
From centre (1,1) the vector to (3,4) is (2,3). Multiply by 2 gives (4,6). Add back to centre: (1+4,1+6) = (5,7).
8. A triangle has a side of length 10 cm. It is reduced by a scale factor of 1/2. What is the length of the corresponding side in the reduced triangle?
Multiply the original length by the scale factor: 10 × 1/2 = 5 cm.
9. Two similar triangles have corresponding side lengths in the ratio 5:8. What is the ratio of their areas?
Area ratio is the square of the linear ratio: 5^2 : 8^2 = 25 : 64.
10. Which statement about similar polygons is true?
Perimeter is a linear measure, so it scales by the same factor as corresponding sides. Areas do not remain equal unless scale factor is 1.
11. If two shapes are similar, which of these must be true?
Similarity preserves angles: corresponding angles are equal, while side lengths are proportional, not necessarily equal.