Question

pentagon ( a^{prime} b^{prime} c^{prime} d^{prime} e^{prime} ) is the image of pentagon ( a b c d e ) after a dilation centered on ( f ).

what is the scale factor of this dilation?

2 a polygon has a perimeter of 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 formula for perimeter after dilation

When a figure is dilated with a scale factor \(k\), the perimeter of the image \(P'\) is related to the perimeter of the original figure \(P\) by the formula \(P'=k\times P\).

Step2: Substitute the given values

We are given that \(P = 12\) units and \(k=\frac{3}{4}\). Then \(P'=\frac{3}{4}\times12\).
Using the multiplication \(\frac{3}{4}\times12=\frac{3\times12}{4}\). Since \(12\div4 = 3\), then \(3\times3=9\).

Answer:

A. 9 units