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 lengths are proportional. In a quadrilateral, the diagonals of a scaled - copy have the same ratio of lengths as the original quadrilateral's diagonals. For a quadrilateral and its scaled - copy, if we consider the diagonals, the ratio of the length of one diagonal in the original to the length of the corresponding diagonal in the scaled - copy is the same for all diagonals. In a quadrilateral \(ABCD\) and its scaled - copy \(PQRS\), the distance between non - adjacent vertices (diagonals) are in proportion. Since \(PQRS\) is a scaled copy of \(ABCD\), the ratio of the length of diagonal \(PR\) to the length of diagonal \(QS\) is \(1:1\) (because the scaling factor is the same for all corresponding lengths).

Step2: Determine the distance from \(Q\) to \(S\)

Given that the distance from \(P\) to \(R\) is 3 units. Since the lengths of corresponding diagonals in a scaled - copy are equal, the distance from \(Q\) to \(S\) is also 3 units.

Answer:

3 units