Question

q1 - accelerated mathematics gr 8 | lesson: describing sequences of transformations
how does applying a dilation with a scale factor of 1.5 affect a triangle’s area?
a. the area increases by 2.25 times.
b. the area increases by 3 times.
c. the area stays the same.
d. the area increases by 1.5 times.
what are the new vertices of a rectangle with original vertices at (1,2), (1,4), (4,4), and (4,2) when transformed to a similar figure by translating it

Explanation:

Step1: Recall dilation - area formula

If the scale - factor of a dilation is $k$, the ratio of the areas of the dilated figure to the original figure is $k^{2}$.

Step2: Identify the scale factor

Here, $k = 1.5$.

Step3: Calculate the area change factor

$k^{2}=1.5^{2}=2.25$. So the area of the triangle increases by 2.25 times.

Answer:

a. The area increases by 2.25 times.