Question

lesson 1 practice 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 is the scale factor. For the top - side, the length of the top - side of \(P\) is \(4\) and of \(Q\) is \(3\). The scale factor \(k=\frac{3}{4}\)

Step2: Find the value of \(y\)

We know that \(x = 6\) (side of \(P\)) and \(y\) is the corresponding side of \(Q\). Using the formula \(y=k\times x\). Substitute \(k = \frac{3}{4}\) and \(x = 6\) into the formula: \(y=\frac{3}{4}\times6=\frac{18}{4}=\frac{9}{2}=4.5\)

Answer:

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