Question

help- A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation.
Which rule could represent this dilation?
A.
(x,y) -->(0.5 - x, 0.5 - y)
B.
(x,y) -->(7 + x, 7 + y)
C.
(x,y) -->(3x, 3y)
D.
(x,y) -->(0.5x, 0.5y)

Answer 1

A dilation of a polygon will result in similar shapes, but the points are multiplied by a factor.

In the context of the question, we are given a polygon that needs to be dilated to make the polygon smaller.

Meaning that each x and y coordinate need to be multiplied by a factor that will make the polygon smaller.

A and B won't achieve this as they are adding or subtracting terms from the x and y values, meaning that they will be transformations and not dilations.

C won't achieve this as multiplying the x and y values by a factor of three will result in a larger polygon.

That means your answer is D, because the factor being multiplied is less than 1, the polygon will be dilated about the origin to make a smaller polygon.

Hope this helps!