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 corresponding distances. In a quadrilateral, the diagonals of a scaled - copy are also in the same ratio as the scale factor. Since $PQRS$ is a scaled copy of $ABCD$, the ratio of corresponding distances is the same. The distance from $P$ to $R$ and the distance from $Q$ to $S$ are corresponding distances (diagonals of the two similar quadrilaterals).

Step2: Determine the answer

Because the quadrilaterals are scaled copies, the distance from $Q$ to $S$ is equal to the distance from $P$ to $R$. Given that the distance from $P$ to $R$ is 3 units, the distance from $Q$ to $S$ is also 3 units.

Answer:

3 units