Question

practice problems
cayden simpson
7 problems
1 polygon q is a scaled copy of polygon p.
a. the value of x is 6, what is the value of y?
b. what is the scale factor?

Explanation:

Step1: Find the scale factor

Since polygon \(Q\) is a scaled copy of polygon \(P\), the ratio of corresponding sides gives the scale factor. For the top - side, if the side of \(P\) is \(4\) and the side of \(Q\) is \(3\), the scale factor \(k=\frac{3}{4}\).

Step2: Find the value of \(y\)

We know that \(y = k\times x\). Given \(x = 6\) and \(k=\frac{3}{4}\), then \(y=\frac{3}{4}\times6=\frac{3\times6}{4}=\frac{18}{4}=\frac{9}{2}=4.5\)

Step3: State the scale factor

The scale factor from \(P\) to \(Q\) is \(\frac{3}{4}\) (by comparing the corresponding sides of the two polygons, for example, the top - side of \(P\) is \(4\) and the top - side of \(Q\) is \(3\), so \(k=\frac{\text{side of }Q}{\text{side of }P}=\frac{3}{4}\))

Answer:

a. \(y = 4.5\)
b. The scale factor is \(\frac{3}{4}\)