Question

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.

Explanation:

Step1: Recall property of scaled - copies

Scaled - copies have proportional side - lengths and distances between corresponding points. The ratio of distances between corresponding points in two scaled - copies is the same for all pairs of corresponding points. In a quadrilateral, the diagonals of scaled - copies are also in the same ratio. Here, PR and QS are diagonals of the scaled - copies PQRS and ABCD respectively.
Since quadrilateral PQRS is a scaled copy of quadrilateral 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

If the distance from P to R is 3 units, and the distances between corresponding diagonals of scaled - copies are equal, then the distance from Q to S is also 3 units.

Answer:

3 units