1.7: Perpendicular diagonals and area of a quadrilateral

4PM1/1/November/2020 — Question 5 · 7 marks

The points P\displaystyle P, Q\displaystyle Q, R\displaystyle R and S\displaystyle S have coordinates (4,7)\displaystyle (4,7), (3,0)\displaystyle (3,0), (10,1)\displaystyle (10,1) and (11,8)\displaystyle (11,8) respectively.
(a) Show, by calculation, that the lines PR\displaystyle PR and QS\displaystyle QS are perpendicular.
(3)
(b) Find the exact lengths of
(i) PR\displaystyle PR,
(ii) QS\displaystyle QS.
(2)
(c) Find the area of the quadrilateral PQRS\displaystyle PQRS.
(2)