WMA11/01 (Edexcel) IAL P1 January 2023, Q2, (Straight Line Graphs: Perpendicular Lines & Rectangles)
The points P, Q and R have coordinates (-3, 7), (9, 11) and (12, 2) respectively.
Prove that angle PQR 90°
(3)
Given that the point S is such that PQRS forms a rectangle,
find the coordinates of S.
(2)
SOLUTION
a-
For angle PQR to be right angle, the product of their gradients must be equals to -1. Therefore, we will first find the gradients of line PQ and QR.
It is better to sketch the lines as shown below for better understanding.
Applying the formula of gradient of a line which is
Check whether their product is equal to -1 or not.
As the product of lines PQ & QR is equals to -1, the angle PQR is proved to be 90°
b-
By looking at the figure, we may see that the horizontal distance between point P and Q is 12. And, the vertical distance between P and Q is 4. Since in a rectangel opposite sides are always equal so the horizontal and vertical distance of S from R or P would be the same.
Therefore, the horizontal distance between S & R must be 12 whereas eth vertical distance must be 4.
Hence, the corrdinates of S is (0,2)
