Question

triangle $\triangle abc$ is the result of dilating $\triangle abc$ about point $b$ by a scale factor of $\dfrac{4}{3}$.
image of coordinate plane with triangle $abc$ and point $b$ at $(-3, 0)$, $a$ at $(3, -3)$, $c$ at $(3, 3)$
determine whether each claim about the properties of $\triangle abc$ and $\triangle abc$ is true or false.

• the lengths of $\overline{ab}$ and $\overline{ab}$ are equal. true/false dropdown
• the areas of $\triangle abc$ and $\triangle abc$ are the same. true/false dropdown

Explanation:

Step1: Recall Dilation Properties

Dilation scales lengths by the scale factor. The scale factor here is $\frac{4}{3}
eq1$, so lengths of corresponding segments (like $\overline{AB}$ and $\overline{A'B'}$) are not equal.

Step2: Recall Area in Dilation

Area scales by the square of the scale factor. Since scale factor $\frac{4}{3}
eq1$, the areas of the triangles (similar figures) will not be the same.

Answer:

The lengths of $\overline{AB}$ and $\overline{A'B'}$ are equal: False
The areas of $\triangle ABC$ and $\triangle A'B'C'$ are the same: False