Question

1. a polygon has perimeter 12 units. it is dilated with a scale factor of $\frac{3}{4}$. what is the perimeter of its image?

a. 9 units
b. 12 units
c. 16 units
d. it cannot be determined.

Explanation:

Step1: Recall the property of dilation on perimeter

When a polygon is dilated, the perimeter of the image is the product of the original perimeter and the scale factor. Let \(P_{original}\) be the original perimeter and \(k\) be the scale factor. Then \(P_{image}=P_{original}\times k\).

Step2: Substitute the given values

Given \(P_{original} = 12\) units and \(k=\frac{3}{4}\). So \(P_{image}=12\times\frac{3}{4}\).
Calculate \(12\times\frac{3}{4}=\frac{12\times3}{4}= 9\).

Answer:

A. 9 units