Question

triangle pro is dilated with origin as the center of dilation using the rule (x, y) -> (10/7x, 10/7y) to create triangle pro.
which statement is true?
triangle pro is larger than triangle pro, because the scale factor is greater than 1.
triangle pro is smaller than triangle pro, because the scale factor is less than 1.
triangle pro is smaller than triangle pro, because the scale factor is greater than 1.
triangle pro is larger than triangle pro, because the scale factor is less than 1.

Explanation:

Step1: Recall the rule of dilation

When a figure is dilated with the rule \((x,y)\to(kx,ky)\), \(k\) is the scale - factor. If \(k > 1\), the image is larger than the original figure. If \(0

Step2: Identify the scale - factor

In the given dilation rule \((x,y)\to(\frac{10}{7}x,\frac{10}{7}y)\), the scale - factor \(k=\frac{10}{7}\). Since \(\frac{10}{7}\approx1.43> 1\)

Answer:

Triangle \(P'R'O'\) is larger than Triangle \(PRO\), because the scale factor is greater than \(1\).