Question

Rectangle PQRS has vertices Q(4,−2) and S(−1,3) . What are the coordinates of vertices P and R ? Note, the vertex labels are located counterclockwise on the graph.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the coordinates of vertices P and R, we can use the fact that opposite sides of a rectangle are equal in length and parallel to each other.

So, we can find the length of side PQ by using the distance formula:

PQ = sqrt((x2 - x1)^2 + (y2 - y1)^2)
PQ = sqrt((4 - (-1))^2 + (-2 - 3)^2)
PQ = sqrt(5^2 + (-5)^2)
PQ = sqrt(25 + 25)
PQ = sqrt(50)
PQ = 5√2

Since the opposite sides of a rectangle are equal in length, we know that RS is also 5√2 units long.

Now, since Q and S are 5 units apart horizontally and also 5 units apart vertically, we can find the coordinates of P and R by moving 5 units in both directions from Q and S, respectively.

Coordinates of P:
x = 4 - 5 = -1
y = -2 + 5 = 3
So, P(-1,3)

Coordinates of R:
x = -1 + 5 = 4
y = 3 - 5 = -2
So, R(4,-2)