Question

Polygon WXYZ

has vertices W(4, 2), X(6, 4)
, Y(2, 3)
, and Z(4, 5)
. Polygon W′X′Y′Z′
is a dilation of WXYZ
with center of dilation (0, 0)
and vertex coordinates W′(2, 1)
, X′(3, 2)
, Y′(1, 1.5)
, and Z′(2, 2.5)
. Find the scale factor of the dilation.

Answer 1

The scale factor of the dilation is 2.

Step-by-step explanation:

To find the scale factor of the dilation, we can compare the corresponding lengths of a side in both polygons.

Let's take the side WX in the original polygon and W'X' in the dilated polygon.

The length of WX is calculated using the distance formula:

√((6-4)^2 + (4-2)^2)

= √8

= 2√2.

The length of W'X' is calculated in the same way:

√((3-2)^2 + (2-1)^2)

= √2.

Therefore, the scale factor of the dilation is :

2√2/√2 = 2.