Question

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

Explanation:

Part 1: Corresponding Side

To find the corresponding side to \( NL \) in the scaled copy, we analyze the congruent - shaped figures (since it's a scaled copy, the figures are similar). By looking at the order of the vertices and the shape of the figures, we can see that the side \( NL \) in the left figure (with vertices \( O, L, N, M \)) corresponds to the side \( TS \) in the right figure (with vertices \( R, S, T, U \)). This is because the order of the vertices and the angles between the sides match when we consider the similarity (scaled copy) of the two figures.

Step 1: Choose a side to measure

Let's choose a side from the left figure, say \( OM \), and its corresponding side \( RU \) from the right figure. First, we need to find the length of \( OM \) and \( RU \) using the grid. Let's assume each grid square has a side length of 1 unit.
For the left figure, let's calculate the length of \( OM \). If we consider the horizontal and vertical distances between \( O \) and \( M \), using the distance formula (or by counting the grid units for horizontal and vertical components). Let's say the horizontal distance is \( x_1 \) and vertical distance is \( y_1 \), and for \( RU \) horizontal distance is \( x_2 \) and vertical distance is \( y_2 \). Alternatively, we can count the number of grid units for a side that is vertical or horizontal. Let's take the vertical side \( NM \) in the left figure. Let's count the number of grid units: if \( NM \) has a length of, say, 2 units (by counting the vertical grid squares). The corresponding vertical side in the right figure, \( TU \), let's count its length. If \( TU \) has a length of 4 units.

Step 2: Calculate the scale factor

The scale factor \( k \) is given by the ratio of the length of the side in the scaled (right) figure to the length of the corresponding side in the original (left) figure. So if the length of \( TU = 4 \) and the length of \( NM = 2 \), then \( k=\frac{4}{2}=2 \). We can verify this with another side. Let's take the side \( OL \) in the left figure and its corresponding side \( RS \) in the right figure. If \( OL \) has a length (calculated from grid) of, say, 3 units and \( RS \) has a length of 6 units, then \( \frac{6}{3}=2 \). So the scale factor is 2.

Answer:

\( TS \)

Part 2: Scale Factor