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 vw?
what is the scale factor?

Explanation:

First Sub - Question: Corresponding Side

In a scaled copy, corresponding sides are those that are in the same relative position in the similar figures. By looking at the orientation and the structure of the two quadrilaterals, we can see that segment \(VW\) in the left figure corresponds to segment \(OQ\) in the right figure (since the left figure's vertices \(V, W\) correspond to the right figure's vertices \(O, Q\) based on the shape and scaling).

Step 1: Determine the length of a side in the original and scaled figure

Let's assume the grid has a side length of 1 unit. First, find the length of a corresponding side. For example, take side \(XV\) in the left figure and side \(PO\) in the right figure. Count the number of grid units. Suppose \(XV\) has a length (vertical) of, say, 3 units (by counting the grids) and \(PO\) has a length of 6 units (by counting the grids in the right figure).

Step 2: Calculate the scale factor

The scale factor \(k\) is given by the ratio of the length of the side in the scaled copy to the length of the corresponding side in the original figure. So \(k=\frac{\text{Length of side in scaled copy}}{\text{Length of side in original figure}}\). If we take the vertical side: let the length of \(XV\) (original) be \(l_1 = 3\) and length of \(PO\) (scaled) be \(l_2=6\). Then \(k = \frac{6}{3}=2\). (We can also check with other sides. For example, if \(VW\) has a length (by counting grids) of, say, 5 units in the original and \(OQ\) has a length of 10 units in the scaled copy, \(\frac{10}{5} = 2\) as well.)

Answer:

The side corresponding to segment \(VW\) is \(OQ\).

Second Sub - Question: Scale Factor