Question

The image of polygon MNOP after transformation is polygon WXYZ. Note that both figures are similar. Each side of MNOP is 2 times as long as the corresponding side of WXYZ. What is the scale factor of the dilation in the similarity transformation?

Answer 1

Answer: 0.5

Explanation:

Given: The image of polygon MNOP after transformation is polygon WXYZ.

let x be any side length of polygon MNOP and y be the side length of polygon WXYZ.

We know that for dilation with scale factor k, the side length of the figure image is k times the side length of the given figure.

Thus, y=kx..........(1)

Since, each side of MNOP is 2 times as long as the corresponding side of WXYZ.

Then
`x=2y\\\Rightarrow\ y=(x)/(2)\\\Rightarrow\ y=0.5x`.........(2)

Therefore, k=0.5 [from (1) and (2)]

Hence, the scale factor of the dilation in the similarity transformation= 0.5

Answer 2

CHOICES: A.)4 B.)0.5 C.)2 D.)0.25

Original figure is MNOP. Dilated figure is WXYZ.
Sides of the original figure is 2 times as long as the sides of the dilated figure. This means that the original figure was compressed.

2x ==>> x
2x * 1/2 ==>> x

The scale factor of the dilation is B.) 0.5