Question

triangle $\triangle abc$ is the result of dilating $\triangle abc$ about point $a$ by a scale factor of $\dfrac{2}{3}$.

determine whether each claim about the properties of $\triangle abc$ and $\triangle abc$ is true or false.

the measures of $\angle b$ and $\angle b$ are equal. \\
true/false

the coordinates of $a$ and $a$ are the same. \\
true/false

Explanation:

Step1: Analyze angle measure claim

Dilation is a similarity transformation. Similar triangles have corresponding angles equal. So $\angle B$ and $\angle B'$ (corresponding angles) should be equal. So the first claim is True.

Step2: Analyze coordinate of A and A' claim

Dilation about point A means point A is the center of dilation. The center of dilation remains unchanged after dilation. So coordinates of A and A' are the same. So the second claim is True.

Answer:

The measures of $\angle B$ and $\angle B'$ are equal: True
The coordinates of A and A' are the same: True