J13

(c)
Use the results for XY and XC to show that points X, Y and C lie on a straight
line.
10. In the diagram, OA = a and OB = b, M is the mid-point of OA and P lies on AB
such that AP = 3 2 AB.
(a) Express the following in terms of a and b: AB, AP, MA and MP
(b) If X lies on OB produced such that OB = BX, express MX in terms of a and b.
(c) Show that MPX is a straight line.
11. X is the mid-point of OD, Y lies on CD such that CY = 4 1 CD, OC = c and OD = d.
(a) Express the following in terms of c and d: CD, CY, CX and OY.
(b) Given that CZ = hCX, express OZ in terms of c, d and h.
(c) If OZ = kOY, find the values of h and k.
12. In the diagram OA = a and OB = b. The points P and Q are such that
AP = 3 1 AB and OQ = 3 1 OA. Express OP and BQ in terms of a and b.
If OC = h OP and BC = k BQ, express OC in two different ways and hence deduce
(a) the values of h and k,
(b) the vector OC in terms of a and b only
(c) the ratio in which C divides BQ.