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Quiz Chapter 5: Congruency, Enlargement and Combined Transformations

10 questions · Form 5 Mathematics Bab 5: Congruency, Enlargement and Combined Transformations

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Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. An image under an enlargement has an area of 108 cm², while the original object has an area of 12 cm². Calculate the positive scale factor k.

  1. A. k = 3
  2. B. k = 9
  3. C. k = 6
  4. D. k = 2
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Answer: A

k² = Area of Image / Area of Object = 10812 = 9. Therefore, k = √9 = 3.

2. An object has an area of 20 cm². It undergoes an enlargement with a scale factor of k = 2. What is the area of the image?

  1. C. 80 cm²
  2. A. 40 cm²
  3. B. 160 cm²
  4. D. 100 cm²
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Answer: C

Area of Image = k² × Area of Object = 2² × 20 = 4 × 20 = 80 cm².

3. If triangle ABC is congruent to triangle DEF, which statement must be true?

  1. A. Corresponding angles are equal and corresponding sides are equal in length
  2. B. Triangle DEF is twice as large as triangle ABC
  3. C. The areas of the two triangles are different
  4. D. The orientations are always reversed
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Answer: A

Congruent shapes are identical in both shape and size; all corresponding angles and sides are equal.

4. Triangle PQR undergoes a rotation of 90° clockwise about the origin. If P is at (3, 1), what are the coordinates of its image P'?

  1. A. (1, -3)
  2. B. (-1, 3)
  3. C. (-3, -1)
  4. D. (3, -1)
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Answer: A

A 90° clockwise rotation about the origin transforms (x, y) into (y, -x). Thus, (3, 1) becomes (1, -3).

5. If a transformation maps a shape onto an image such that orientation is reversed but size and shape remain unchanged, the transformation is a...

  1. B. Reflection
  2. A. Rotation
  3. C. Translation
  4. D. Enlargement
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Answer: B

Reflection preserves distance and shape (isometry) but reverses the orientation (lateral inversion) of the shape.

6. An object has an area of 15 cm². It is enlarged with a scale factor of k = -3. What is the area of the resulting image?

  1. A. 135 cm²
  2. B. -135 cm²
  3. C. 45 cm²
  4. D. -45 cm²
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Answer: A

Area of Image = k² × Area of Object = (-3)² × 15 = 9 × 15 = 135 cm². (Area is always positive).

7. What is a pattern called when repeated geometric shapes cover a surface completely without gaps or overlaps?

  1. A. Tessellation
  2. B. Differentiation
  3. C. Interpolation
  4. D. Extrapolation
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Answer: A

A tessellation is a tiling pattern made of repeating shapes covering a plane without gaps or overlaps.

8. In a diagram, shape Q is the image of shape P under an enlargement with scale factor k = 4. If the area of shape Q is 160 cm², calculate the area of the shaded region representing Q excluding P.

  1. B. 150 cm²
  2. A. 10 cm²
  3. C. 140 cm²
  4. D. 120 cm²
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Answer: B

Area of Q = k² × Area of P => 160 = 16 × Area of P => Area of P = 10 cm². Area of Shaded Region = Area of Q - Area of P = 160 - 10 = 150 cm².

9. Which of the following transformations is NOT an isometry?

  1. A. Enlargement
  2. B. Translation
  3. C. Reflection
  4. D. Rotation
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Answer: A

Enlargement changes the size of the shape (unless k = 1), so it is not an isometry. Translation, reflection, and rotation preserve both shape and size.

10. Two triangles have three pairs of equal corresponding sides. Which congruency criterion applies?

  1. A. Side-Side-Side (SSS)
  2. B. Side-Angle-Side (SAS)
  3. C. Angle-Side-Angle (ASA)
  4. D. Angle-Angle-Angle (AAA)
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Answer: A

When all three pairs of corresponding sides are equal, the triangles are congruent by the Side-Side-Side (SSS) criterion.

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