1.22: Past-paper question 2

4PM1/2R/June/2025 — Question 2 · 10 marks

The point P\displaystyle P has coordinates (−7,3)\displaystyle (-7, 3) and the point Q\displaystyle Q has coordinates (3,18)\displaystyle (3, 18)
The point R\displaystyle R divides the line PQ\displaystyle PQ in the ratio 2:3\displaystyle 2:3
The line l\displaystyle l passes through R\displaystyle R and is perpendicular to the line PQ\displaystyle PQ
(a) Find an equation of line l\displaystyle l
Give your answer in the form ay+bx+c=0\displaystyle ay + bx + c = 0 where a,b\displaystyle a, b and c\displaystyle c are integers.
(5)
The line l\displaystyle l crosses the x\displaystyle x-axis at the point S\displaystyle S
(b) Find the area of triangle QRS\displaystyle QRS
(5)