Question

the figure on the right is a scaled copy of the figure on the left.
answer attempt 1 out of 2
which side in the figure on the right corresponds to segment om?
what is the scale factor?

Explanation:

First Sub - Question: Corresponding Side to \( OM \)

In a scaled copy, corresponding sides are the sides that are in the same relative position in the original and the scaled figure. Looking at the two figures, the original figure has segment \( OM \), and in the scaled (right) figure, the side that is in the same relative position as \( OM \) is \( VU \). This is because the vertices of the original figure ( \( O, M, L, N, P \)) correspond to the vertices of the scaled figure ( \( V, U, T, W, X \)) in order, so the side connecting the first two corresponding vertices ( \( O \) to \( M \) in original, \( V \) to \( U \) in scaled) is the corresponding side.

Step 1: Choose a pair of corresponding sides

Let's choose a side from the original figure and its corresponding side from the scaled figure. For example, let's consider the horizontal segment \( NP \) in the original figure and its corresponding segment \( WX \) in the scaled figure.

Step 2: Count the length of \( NP \)

Looking at the grid, if we assume each grid square has a side length of 1 unit. Let's count the number of grid units for \( NP \). Suppose \( NP \) has a length of, say, 3 units (we can count the horizontal squares it spans).

Step 3: Count the length of \( WX \)

Now, count the length of \( WX \) in the scaled figure. If \( WX \) spans 6 units (double the length of \( NP \)), then the scale factor \( k=\frac{\text{Length of side in scaled figure}}{\text{Length of corresponding side in original figure}} \).
Alternatively, we can look at the vertical or other sides. Let's take the side \( OM \) and \( VU \). If \( OM \) has a length (by counting grid units) of, say, 2 units, and \( VU \) has a length of 4 units. Then the scale factor \( k = \frac{4}{2}=2 \).
(In general, by observing the grid and the relative sizes, the scale factor is 2 as the scaled figure is twice as large as the original in terms of side lengths.)

Answer:

\( VU \)

Second Sub - Question: Scale Factor