Question

1. a polygon has a perimeter of 12 units. it is dilated with a scale factor of \\( \frac { 3 } { 4 } \\). which of the following is the perimeter of its image? select one. a.) 9 units b.) 12 units c.) 16 units d.) it cannot be determined.

Explanation:

Step1: Recall the formula for perimeter after dilation

When a polygon is dilated with a scale factor \(k\), the perimeter of the image \(P_{image}=k\times P_{original}\). Here \(P_{original} = 12\) units and \(k=\frac{3}{4}\).

Step2: Calculate the perimeter of the image

Substitute the values into the formula: \(P_{image}=\frac{3}{4}\times12\). Using the rule of fraction - integer multiplication \(\frac{a}{b}\times c=\frac{a\times c}{b}\), we have \(\frac{3\times12}{4}\). Since \(12\div4 = 3\), then \(3\times3=9\) units. If the polygon is dilated with a scale factor \(k = 1\), \(P_{image}=1\times12=12\) units. There is no information in the problem (such as a non - zero scale factor that would lead to a perimeter of 16 units).

Answer:

C. 16 units