Paper 2 · November 2017 (topical set) · Vector Geometry
In the diagram, OQR, OMP, PTQ and RTM are straight lines such that OM = (1/3)OP and PT = (3/4)PQ. It is given that OP = 12a and OQ = 4b. (a) Express as simply as possible, in terms of a and/or b (i) PQ, [1] (ii) PT, [1] (iii) OT, [1] (iv) MT. [2] (b) It is given that MR = h MT. Express OR in terms of a and/or b and a constant h. [2] (c)(i) It is given that OR = k OQ. Express OR in terms of a and/or b and a constant k. [1] (ii) Use the expressions for OR in (b) and (c)(i) to find the values of h and k. [3] (d) Write down the numerical value of MT:TR. [1]
Model answer
(a)(i) PQ = 4b - 12a (ii) PT = 3b - 9a (iii) OT = 3a + 3b (iv) MT = 3b - a; (b) OR = (4 - h)a + 3h b; (c)(i) OR = 4k b (ii) h = 4, k = 3; (d) 1 : 3
Also accepted: 4b - 12a; 3b - 9a; 3(a + b); 3b - a; (4-h)a + 3hb; 4kb; h = 4, k = 3; 1:3, h = 4, k = 3, MT:TR = 1 : 3, 1:3, 1 : 3, 4b - 12a; 3b - 9a; 3a + 3b; 3b - a; (4 - h)a + 3hb; 4kb; 4, 3; 1:3
ZIMSEC Mathematics 4030/2, November 2017, Q12, via the Topical Collection