Question

geometry
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. identify the points in figure 1 that correspond to the points q and s in figure 2. label them b and d.
b. what is the scale factor? how do you know?
expressions and equations
the art club is going on a two - day trip to the state fair that includes a concert after the 2nd day. the trip costs $52 for each person. included in that price is $11 for a concert ticket and the cost of a pass for each day. how much and the cost of a pass for one day cost? explain how you

Explanation:

Step1: Identify corresponding points

In scaled - copies, relative positions of points are maintained. By observing the relative positions of points in Figure 1 and Figure 2, we can see that the point in Figure 2 corresponding to point A in Figure 1 is the left - most point of the smaller shape in Figure 2, label it P. The point in Figure 2 corresponding to point C in Figure 1 is the top - right point of the smaller shape in Figure 2, label it R. The point in Figure 1 corresponding to point Q in Figure 2 is the top - right point of the larger shape in Figure 1, label it B. The point in Figure 1 corresponding to point S in Figure 2 is the bottom - right point of the larger shape in Figure 1, label it D.

Step2: Calculate scale factor

To find the scale factor, we can compare the lengths of corresponding line segments. Let's consider the horizontal distance between two corresponding points. For example, if we consider a horizontal line segment in Figure 1 and its corresponding horizontal line segment in Figure 2. Suppose a horizontal line segment in Figure 1 has a length of 2 units (counting the grid squares), and the corresponding horizontal line segment in Figure 2 has a length of 4 units. The scale factor $k$ is given by the ratio of the lengths of corresponding line segments in the scaled - copy (Figure 2) and the original figure (Figure 1). So, $k=\frac{\text{Length in Figure 2}}{\text{Length in Figure 1}}$. If we take the ratio of the side - lengths of the two similar shapes, by counting the grid squares, we find that the scale factor is 2. We know this because each side - length in Figure 2 is twice as long as the corresponding side - length in Figure 1.

Answer:

a. In Figure 2, the point corresponding to A is P and the point corresponding to C is R. In Figure 1, the point corresponding to Q is B and the point corresponding to S is D.
b. The scale factor is 2. We know this because each side - length in Figure 2 is twice as long as the corresponding side - length in Figure 1 when comparing corresponding line segments by counting the grid squares.