IGCSE Mathematics 0580/04/SP/20 Q6
OPQR is a rectangle and O is the origin.
M is the midpoint of RQ and PT : TQ = 2 : 1.
OP = P and OR = r.
(a) Find, in terms of p and/or r, in its simplest form
(ii) MT ,
(iii) OT .
(b) RQ and OT are extended and meet at U.
Find the position vector of U in terms of p and r.
Give your answer in its simplest form.
(c) MT = −(2k/-k) and MT = 180.
Find the positive value of k.