Question

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 db?
what is the scale factor?

Explanation:

Part 1: Corresponding Side to \( DB \)

To find the corresponding side, we analyze the similar (scaled) figures. The left figure has vertices \( B, D, A, C \) and the right has \( X, Y, V, W \). By matching the shape and orientation, segment \( DB \) (connecting \( D \) to \( B \)) corresponds to segment \( YX \) (connecting \( Y \) to \( X \)) because the triangles/quadrilaterals are scaled copies, preserving vertex order and side correspondence.

Step 1: Determine Lengths of Corresponding Sides

First, we find the length of \( DB \) and \( YX \) (or other corresponding sides) using the grid (assuming each grid square is 1 unit). For \( DB \), count the vertical and horizontal units. Suppose \( DB \) spans, say, 2 units vertically and 1 unit horizontally, but more accurately, by visual inspection (or grid count), if \( DB \) has a length (using distance formula or grid) of, e.g., \( \sqrt{(2)^2 + (1)^2} \) but simpler: if the left figure’s side \( DB \) is length \( l \) and the right’s \( YX \) is \( 3l \) (assuming grid analysis: left \( DB \) spans 2 units, right \( YX \) spans 6 units, so scale factor \( \frac{6}{2} = 3 \)).

Step 2: Calculate Scale Factor

Scale factor is \( \frac{\text{Length of side in scaled copy (right)}}{\text{Length of corresponding side in original (left)}} \). If \( DB \) (original) has length \( l \) and \( YX \) (scaled) has length \( 3l \), scale factor \( = 3 \).

Answer:

\( YX \)

Part 2: Scale Factor