10 questions · Form 5 Mathematics Bab 5: Congruency, Enlargement and Combined Transformations
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?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. 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?
Answer: C
Area of Image = k² × Area of Object = 2² × 20 = 4 × 20 = 80 cm².
2. 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.
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.
3. If triangle ABC is congruent to triangle DEF, which statement must be true?
Answer: A
Congruent shapes are identical in both shape and size; all corresponding angles and sides are equal.
4. 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.
Answer: A
k² = Area of Image / Area of Object = 10812 = 9. Therefore, k = √9 = 3.
5. Under a combined transformation MN acting on shape P, which transformation is applied first?
Answer: B
In combined transformation notation MN(P), the transformation written on the right (N) is executed first, followed by M.
6. Why does the criterion Angle-Angle-Angle (AAA) NOT prove that two triangles are congruent?
Answer: A
AAA guarantees that two triangles have the same shape (similar), but their sizes can differ, so they are not necessarily congruent.
7. What does a negative scale factor (e.g., k = -2) indicate about the image under an enlargement?
Answer: A
A negative scale factor produces an inverted image on the opposite side of the center of enlargement.
8. Which criterion guarantees congruency between two right-angled triangles when their hypotenuses and one pair of corresponding legs are equal?
Answer: C
The RHS (Right angle-Hypotenuse-Side) criterion establishes congruency specifically for right-angled triangles.
9. Which of the following transformations is NOT an isometry?
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. Which of the following scale factors represents an enlargement that produces an image smaller than the object without inversion?
Answer: C
When 0 < k < 1, the image is smaller than the object and retains the same orientation.