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

(x, y) → (4/5 x, 4/5 y)

Question:

The answer choices to determine the rule that represent the dilation were not given. Let's consider the following question:

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) → (x − 7, y − 7)

C) (x, y) → ( 5/4 x, 5/4 y)

D) (x, y) → (4/5 x, 4/5 y)

Step-by-step explanation:

To determine the rule that could represent the dilation, we would multiply each coordinate by a dilation factor (a constant) to create a dilation. Since the dilation would be used to create a smaller polygon, the constant multiplied with the coordinates of x and y would be less than 1.

Let's check the options out.

In option (A), the coordinates is subtracted from the constant (0.5).

In option (B), the constant (7) is subtracted from the coordinates.

In option (C), the coordinates are multiplied by constant (5/4).

But 5/4 = 1.25. This is greater than 1.

In option (D), the coordinates are multiplied by constant (4/5).

4/5 = 0.8

The constant multiplied with the coordinates of x and y is less than 1 in option (D) = (x, y) → (4/5 x, 4/5 y)

4/5 = 0.8

0.8 is less than 1