Question

figure 2 is a scaled copy of figure 1.
a. identify the points in figure 2 that correspond to the points a and c in figure 1. label them p and r. what is the distance between p and r?
b. identify the points in figure 1 that correspond to the points q and s in figure 2. label them b and d. what is the distance between b and d?
c. what is the scale factor that takes figure 1 to figure 2?
d. g and h are two points on figure 1, but they are not shown. the distance between g and h is 1. what is the distance between the corresponding points on figure 2?

Explanation:

Step1: Identify corresponding points in part a

Since Figure 2 is a scaled - copy of Figure 1, by comparing the shapes and positions, the point in Figure 2 corresponding to point A in Figure 1 is the left - most point of the larger shape. Let's call it P. The point corresponding to C is the middle - top point of the larger shape. Let's call it R. To find the distance between P and R, count the horizontal and vertical distances on the grid. The horizontal distance \(x = 4\) units and the vertical distance \(y=3\) units. Using the distance formula \(d=\sqrt{x^{2}+y^{2}}\), we have \(d = \sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5\) units.

Step2: Identify corresponding points in part b

The points in Figure 1 corresponding to Q and S in Figure 2 are the right - most and bottom - right points of the smaller shape respectively. Let's call them B and D. Counting the horizontal and vertical distances on the grid, the horizontal distance \(x = 2\) units and the vertical distance \(y = 2\) units. Using the distance formula \(d=\sqrt{x^{2}+y^{2}}\), we get \(d=\sqrt{2^{2}+2^{2}}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\) units.

Step3: Find the scale factor in part c

Choose a pair of corresponding line - segments. For example, if we consider the horizontal distance from the left - most point to the next vertex. In Figure 1, it is 2 units and in Figure 2, it is 4 units. The scale factor \(k=\frac{\text{length in Figure 2}}{\text{length in Figure 1}}\). So \(k = 2\).

Step4: Find the distance in part d

Since the scale factor from Figure 1 to Figure 2 is 2, if the distance between G and H in Figure 1 is 1, then the distance between the corresponding points in Figure 2 is \(1\times2=2\).

Answer:

a. P and R are the corresponding points. Distance between P and R is 5 units.
b. B and D are the corresponding points. Distance between B and D is \(2\sqrt{2}\) units.
c. The scale factor is 2.
d. The distance between the corresponding points is 2 units.