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?

Explanation:

Step1: Find corresponding points

Since Figure 2 is a scaled - copy of Figure 1, the point in Figure 2 that corresponds to point A in Figure 1 is the left - most point of the triangle in Figure 2. Let's label it P. The point in Figure 2 that corresponds to point C in Figure 1 is the middle point of the triangle in Figure 2. Let's label it R.

Step2: Use distance formula

Assume each grid square has a side - length of 1 unit. If the coordinates of P are \((x_1,y_1)\) and of R are \((x_2,y_2)\), the distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Counting the grid squares, if we assume P is at \((x_1,y_1)=(3,2)\) and R is at \((x_2,y_2)=(5,4)\), then \(x_2 - x_1=2\) and \(y_2 - y_1 = 2\).
\[d=\sqrt{(5 - 3)^2+(4 - 2)^2}=\sqrt{2^2+2^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\]

Answer:

The distance between P and R is \(2\sqrt{2}\) units.