Question

The coordinates of the vertices of rectangle PQRS are shown below. Which of the following points is not on rectangle PQRS?

a) P : (–2, –2)
b) Q : (–2, 3)
c) R : (5, 3)
d) S : (5, –2)

Answer 1

The point that is not on the rectangle PQRS is Q: (-2, 3).

Step-by-step explanation:

In a rectangle, opposite sides are parallel and equal in length. Therefore, we need to check if the distances between points P and Q, Q and R, and R and S are equal. We can use the distance formula to calculate the distances between these points:

1. PQ: √((-2 - (-2))^2 + (3 - (-2))^2) = √(0 + 25) = √25 = 5
2. QR: √((-2 - 5)^2 + (3 - 3)^2) = √((-7)^2 + 0) = √49 = 7
3. RS: √((5 - 5)^2 + (-2 - 3)^2) = √(0 + 25) = √25 = 5

Since the distances between all pairs of consecutive points are not equal, the point that is not on the rectangle is Q: (-2, 3).