Question

spaced practice

1. triangle xyz has been enlarged with p as the center of dilation to form △xyz. identify the equivalent ratios that are equal to the scale factor.
2. a triangle is dilated with center of dilation at point u. point e is a vertex of the triangle, and point e is the corresponding vertex of the image. if ue = 2 centimeters and ue = 10 centimeters, what is the scale factor?

the scale factor:

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ of a dilation with center $O$ and a point $A$ and its image $A'$ is given by $k=\frac{OA'}{OA}$.

Step2: Solve for question 1

For a dilation with center $P$ transforming $\triangle XYZ$ to $\triangle X'Y'Z'$, the scale - factor is the ratio of the distance from the center of dilation to a point on the image to the distance from the center of dilation to the corresponding point on the pre - image. So, $\frac{PX'}{PX}=\frac{PY'}{PY}=\frac{PZ'}{PZ}$.

Step3: Solve for question 2

Given $UE = 2$ cm and $UE'=10$ cm. Using the scale - factor formula $k=\frac{UE'}{UE}$. Substitute the values: $k=\frac{10}{2}=5$.

Answer:

1. $\frac{PX'}{PX}=\frac{PY'}{PY}=\frac{PZ'}{PZ}$
2. 5