Question

two figures are dilations of each other if they are similar. use similarity to check if figure ( m ) is a dilation of figure ( m ).
similar figures:

• corresponding sides are proportional.
• corresponding angles are equal.

are the corresponding sides of figures ( m ) and ( m ) proportional?
each side of figure ( m ) is times as long as the correspon de of figure ( m ), so the corresp sides proportiona

Explanation:

Step1: Count the side lengths

Count the side lengths of figure \(M\) and \(M'\) using the grid. For figure \(M\), assume a side length (e.g., horizontal or vertical side between two adjacent grid points) as \(1\) unit. For figure \(M'\), measure the corresponding sides.

Step2: Calculate the ratio

Let's take a side of \(M\) as \(x\) units (by counting grid - squares, say \(x = 1\) for a basic segment of \(M\)) and the corresponding side of \(M'\) as \(y\) units. If we count, we find that each side of \(M'\) is \(3\) times as long as the corresponding side of \(M\). For example, if a side of \(M\) spans \(1\) grid - square (length \(1\)), the corresponding side of \(M'\) spans \(3\) grid - squares (length \(3\)).

Answer:

Each side of figure \(M'\) is \(3\) times as long as the corresponding side of figure \(M\), so the corresponding sides are proportional.