Question

△xyz is a dilation of △xyz. identify the type of dilation and find the scale factor.

Explanation:

Step1: Determine the type of dilation

Since $\triangle X'Y'Z'$ is smaller than $\triangle XYZ$, it is a reduction.

Step2: Find the scale - factor

Let's consider the distance between points. For example, the $y$ - coordinate of $Y$ is 6 and the $y$ - coordinate of $Y'$ is 2. The scale factor $k$ can be found by taking the ratio of the corresponding side lengths. If we consider the vertical distance from the origin to the points on the $y$ - axis for the two triangles, $k=\frac{Y'_y}{Y_y}=\frac{2}{6}=\frac{1}{3}$. We can also check with other corresponding points. For example, the $y$ - coordinate of $Z$ is 3 and the $y$ - coordinate of $Z'$ is 1, and $\frac{Z'_y}{Z_y}=\frac{1}{3}$.

Answer:

The type of dilation is a reduction and the scale factor is $\frac{1}{3}$.