Question

q3 - mathematics gr 8 - section 1 | lesson: describing sequences of transformations for similar figures

1. how does applying a dilation with a scale factor of 1.5 affect a triangles area?

a. the area increases by 2.25 times.
b. the area increases by 1.5 times.
c. the area increases by 3 times.
d. the area stays the same.

1. which sequence of transformations maps a rectangle from (1,2), (1,4), (3,4), and (3,2) to (-2,-4), (-2,-8), (-6,-8), and (-6,-4)?

a. translation by 9 units left and 12 units down
b. dilation by scale factor of -2
c. translation by 2 units right
d. dilation by scale factor of 2

1. what is the result of applying a dilation with a scale factor of 3 to a rectangle with side lengths of 2 units and 4 units?

a. the new rectangle has side lengths of 3 units and 6 units.
b. the new rectangle has side lengths of 6 units and 12 units.
c. the new rectangle has side lengths of 4 units and 8 units.

Explanation:

Step1: Solve first dilation-area question

For a dilation with scale factor $k$, area scales by $k^2$. Here $k=1.5$, so $1.5^2=2.25$.

Step2: Solve second transformation question

Check if each original coordinate $(x,y)$ becomes $(-2x,-2y)$:

• $(1,2) \to (-2(1), -2(2))=(-2,-4)$
• $(1,4) \to (-2(1), -2(4))=(-2,-8)$
• $(3,4) \to (-2(3), -2(4))=(-6,-8)$
• $(3,2) \to (-2(3), -2(2))=(-6,-4)$

This matches the target coordinates, so scale factor is -2.

Step3: Solve third dilation-side length question

Multiply each original side length by scale factor 3:

• $2 \times 3 = 6$
• $4 \times 3 = 12$

Answer:

1. a. The area increases by 2.25 times.
2. b. dilation by scale factor of -2
3. b. The new rectangle has side lengths of 6 units and 12 units.