Question

15

2. The points P, Q and R have coordinates (-3, 7), (9, 11) and (12, 2) respectively.
(a) Prove that angle PQR = 90°
Given that the point S is such that PQRS forms a rectangle,
(b) find the coordinates of S.

Answer 1

The product of the slope is -1, we have shown that angle PQR is a right angle.

The coordinate of S is (-2, 0)

How to prove that PQR is right triangle

To prove that angle PQR is a right angle, we can show that the slope of PQ multiplied by the slope of QR is equal to -1.

Slope of PQ

= (7 - 11) / (-3 - 9)

= -4 / -12

= 1/3

Slope of QR

= (2 - 11) / (12 - 9)

= -9 / 3

= -3

Now check: 1/3 * -3 = -1

b), since PQRS forms a rectangle, opposite sides are parallel and have the same slope.

Using construction, by projecting parallel lines, point S is (-2, 0)