Question

problem 2 here is quadrilateral abcd. quadrilateral pqrs is a scaled copy of quadrilateral abcd. point p corresponds to a, q to b, r to c, and s to d. if the distance from p to r is 3 units, what is the distance from q to s? explain your reasoning. problem 3 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?

Explanation:

Step1: Recall property of scaled - copies

In scaled - copies of geometric figures, corresponding distances are in the same ratio. In a quadrilateral, the diagonals of a scaled - copy have the same ratio as the original quadrilateral. For a quadrilateral \(ABCD\) and its scaled - copy \(PQRS\), if \(PR\) and \(QS\) are diagonals, and since it's a scaled - copy, the ratio of corresponding lengths is the same. The diagonals of similar (scaled) quadrilaterals are in proportion. In this case, the distance between opposite vertices in the scaled - copy has the same relationship as in the original. Since \(PQRS\) is a scaled copy of \(ABCD\), the distance from \(Q\) to \(S\) is equal to the distance from \(P\) to \(R\).

Step2: Determine the distance

Given that the distance from \(P\) to \(R\) is 3 units, the distance from \(Q\) to \(S\) is also 3 units.

Answer:

3 units