Question

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

Explanation:

For the corresponding side:

In scaled copies, corresponding sides are those that have the same relative position and shape. The left figure has segment \( XZ \), and in the right figure (scaled copy), the side with the same relative position and slope as \( XZ \) is \( LN \). This is because the figures are similar (scaled copies), so the sides that are "slanted" in the same way correspond.

Step1: Determine lengths of corresponding sides

First, we can count the grid units for a horizontal or vertical side. Let's take the horizontal side \( WY \) (or \( XW \), but \( WY \) is vertical? Wait, no, \( WY \) is vertical? Wait, looking at the grid, let's take the length of \( XY \)? Wait, better to take a horizontal side. Let's take \( ZY \) on the left: let's count the grid squares. Suppose \( ZY \) is, say, 6 units (counting the grid), and \( NM \) on the right is 3 units. Or another side: \( WY \) (vertical) on the left: let's say it's 4 units, and \( OM \) on the right is 2 units.

Step2: Calculate scale factor

Scale factor is the ratio of length of scaled copy side to original side. So if \( ZY \) (original) is 6 and \( NM \) (scaled) is 3, then scale factor \( = \frac{3}{6} = \frac{1}{2} \). Alternatively, \( WY \) (original) length: let's count the vertical grid. From \( Y \) to \( W \), suppose it's 4 units (from y-coordinate, say, 4 grids), and \( M \) to \( O \) is 2 units. So \( \frac{2}{4} = \frac{1}{2} \).

Answer:

The side corresponding to segment \( XZ \) is \( LN \).

For the scale factor: