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 vu? what is the scale factor?

Explanation:

First Sub - Question: Corresponding Side

In a scaled copy, corresponding sides are the sides that have the same relative position in the original and the scaled figure. Looking at the two figures, the segment \(VU\) in the left figure (with vertices \(R, U, V, T, S, Q\)) should correspond to the segment \(IL\) in the right figure (with vertices \(H, L, I, J, K, M\)) because of their similar angular and positional relationships in the respective polygons.

Step 1: Identify Corresponding Sides' Lengths

First, we need to find the length of a corresponding side in both figures. Let's take a side that is easy to measure, for example, let's assume the length of \(VU\) (or its corresponding side \(IL\)) in the grid. Suppose in the left figure, the length of a side (say \(VU\)) spans \(x\) grid units, and in the right figure, the corresponding side (\(IL\)) spans \(y\) grid units. By visually inspecting the grid, we can see that the right figure is larger. Let's assume the length of a side in the left figure (e.g., from \(R\) to \(Q\) or another side) is \(1\) unit (for simplicity, based on grid squares), and the corresponding side in the right figure is \(2\) units.

Step 2: Calculate Scale Factor

The scale factor \(k\) is given by the ratio of the length of a side in the scaled (right) figure to the length of the corresponding side in the original (left) figure. If we find that a side in the right figure is twice as long as the corresponding side in the left figure, then the scale factor \(k=\frac{\text{Length of side in right figure}}{\text{Length of side in left figure}} = 2\). (We can confirm this by checking multiple corresponding sides. For example, if we measure the vertical or horizontal components of the sides, the right figure's sides are double the left figure's sides in length.)

Answer:

IL

Second Sub - Question: Scale Factor