Question

Find the coordinates of point S, which, along with points P, Q, and R, will form the vertices of a quadrilateral with opposite sides parallel.

Given points:
P(3, 5)
Q(7, 2)
R(1, 1)

a) S(5, 8)
b) S(2, 7)
c) S(4, 4)
d) S(6, 3)

Answer 1

To find the coordinates of point S, we need to calculate the slopes of the sides formed by points P, Q, and R.

Step-by-step explanation:

To find the coordinates of point S, we need to recall the properties of a quadrilateral with opposite sides parallel. In such a quadrilateral, the opposite sides are parallel and have the same slope. Looking at points P, Q, and R, we can calculate the slopes of the sides formed by these points.

Let's calculate the slopes:

Slope of PQ: (2-5)/(7-3) = -3/4

Slope of QR: (1-2)/(1-7) = 1/6

Slope of RP: (5-1)/(3-1) = 2/2 = 1

Since the slopes of opposite sides are not equal, the given points P, Q, and R do not form a quadrilateral with opposite sides parallel. Therefore, we cannot determine the coordinates of point S based on the given information.