Similarity and enlargement · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Similar shapes and enlargement

Mathematics · Geometry · ages 12-14
Name ______________________   Date ____________

  1. Rectangle A is 4 cm wide and 6 cm long. Rectangle B is an enlargement of A, and it is 8 cm wide and 12 cm long. What is the scale factor of the enlargement?

    • 2
    • 3
    • 4
    • 6

  2. What is the name of the fixed point you enlarge a shape from?

    • Scale factor
    • Centre of enlargement
    • Vertex

  3. In an enlargement, the angles of the shape change to match the new size.

    Circle one:   True   False

  4. A point at (2, 4) is enlarged by scale factor 2 from the origin. Where does it land?

    • (4, 8)
    • (2, 8)
    • (4, 4)

  5. To make a poster, Jeff enlarges a photograph by a scale factor of 3. The photograph is 4 inches wide and 5 inches long. What is the area of the poster in square inches?

    Answer: ______________

  6. A small rectangle is 2 cm by 3 cm. Which of these rectangles is an enlargement of it?

    • 6 cm by 9 cm
    • 4 cm by 5 cm
    • 6 cm by 7 cm
    • 4 cm by 9 cm

  7. A triangle has vertices at (1, 1), (3, 1) and (1, 3). It is enlarged by scale factor 2 from the origin. Where does the vertex (3, 1) move to?

    • (6, 2)
    • (3, 2)
    • (6, 1)

  8. Two similar rectangles have matching sides of 3 cm and 9 cm. What is the scale factor from the small one to the big one?

    ?
    • 3
    • 6
    • 9

  9. Priya wants to enlarge the point (4, 4) by scale factor 3 from a centre at (2, 2), which is not the origin. She just multiplies both coordinates by 3 and gets (12, 12). What is the correct new point?

    • (8, 8)
    • (12, 12)
    • (6, 6)

  10. A shape is enlarged with a scale factor of 2. What happens to its area?

    • It stays the same
    • It doubles
    • It becomes 4 times bigger
    • It becomes 8 times bigger
LightMySky · lightmysky.comW1-mt_y-BuQAfw4B-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Similar shapes and enlargement W1-mt_y-BuQAfw4B-s1

  1. 2 · The scale factor is 2 because every side of rectangle B is exactly 2 times the matching side of rectangle A.
  2. Centre of enlargement · The centre of enlargement is the fixed point. Every corner moves away from it by the scale factor.
  3. False · Angles stay exactly the same. Only the side lengths scale up or down.
  4. (4, 8) · Multiply each coordinate by the scale factor: 2 × 2 = 4 and 4 × 2 = 8.
  5. 180 · The poster is 12 inches by 15 inches, so its area is 180 square inches.
  6. 6 cm by 9 cm · Only 6 cm by 9 cm works, because both sides are multiplied by the same number, 3.
  7. (6, 2) · Multiply both coordinates by 2: (3 × 2, 1 × 2) = (6, 2).
  8. 3 · Divide the new side by the matching original side: 9 ÷ 3 = 3.
  9. (8, 8) · Find the vector from the centre to the point, (2, 2), scale it by 3 to get (6, 6), then add it back to the centre: (2 + 6, 2 + 6) = (8, 8).
  10. It becomes 4 times bigger · Both the length and the width are multiplied by 2, and 2 x 2 = 4, so the area becomes 4 times bigger.
Worksheet · LightMySky