WMA11/01 Jan 2023, Question 2: Perpendicular Lines
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 5 marks
The question, in short
Given points P(−3, 7), Q(9, 11) and R(12, 2), show angle PQR is 90°, then use the rectangle PQRS to find S's coordinates.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 3 marks
Show that angle PQR equals 90° using the coordinates of P, Q and R.
- 1Gradient PQ = (11 − 7)/(9 + 3) = 4/12 = 1/3
- 2Gradient QR = (11 − 2)/(9 − 12) = 9/(−3) = −3
- 3(1/3) × (−3) = −1, so PQ is perpendicular to QR and angle PQR = 90°
AnswerShown: gradient PQ = 1/3, gradient QR = −3, and (1/3) × (−3) = −1, so angle PQR = 90°
Part (b) · 2 marks
Given PQRS is a rectangle, work out the coordinates of point S.
- 1Vector QR = (12 − 9, 2 − 11) = (3, −9)
- 2PS = QR, so S = (−3 + 3, 7 − 9) = (0, −2)
AnswerS(0, −2)
Stuck on a step? Read the free lesson: Perpendicular Lines
Practise more perpendicular lines questions
Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on perpendicular lines
Also searched as: WMA11 January 2023 · WMA11/01 · wma11 jan23 · IAS Maths Pure Mathematics 1 January 2023 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.