Question

the triangle ( bcd ) is a dilation of the triangle ( bcd ). what is the scale factor of the dilation?
simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Find the length of a side in the original triangle and the corresponding side in the dilated triangle

Let's consider the horizontal side \(CD\) in \(\triangle BCD\) and \(C'D'\) in \(\triangle B'C'D'\).
The length of \(CD\): \(C(-9,-4)\) and \(D(-6,-8)\). Using the distance formula for horizontal - side (since \(y\) - coordinates are the same for a horizontal side in this case, we can just find the difference in \(x\) - coordinates). The length of \(CD=\vert-9-(-6)\vert = 3\).
The length of \(C'D'\): \(C'(-4,-2)\) and \(D'(-3,-4)\). The length of \(C'D'=\vert-4 - (-3)\vert=1\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}\).
\(k = \frac{1}{3}\)

Answer:

\(\frac{1}{3}\)