Date | May 2007 | Marks available | 4 | Reference code | 07M.1.sl.TZ0.10 |
Level | SL only | Paper | 1 | Time zone | TZ0 |
Command term | Determine | Question number | 10 | Adapted from | N/A |
Question
P (4, 1) and Q (0, –5) are points on the coordinate plane.
Determine the
(i) coordinates of M, the midpoint of P and Q.
(ii) gradient of the line drawn through P and Q.
(iii) gradient of the line drawn through M, perpendicular to PQ.
The perpendicular line drawn through M meets the y-axis at R (0, k).
Find k.
Markscheme
(i) (2, – 2) parentheses not required. (A1)
(ii) gradient of PQ =(−5−10−4)=64=32(1.5) (M1)(A1)
(M1) for gradient formula with correct substitution
Award (A1) for y=32x−5 with no other working
(iii) gradient of perpendicular is −23 (A1)(ft) (C4)
[4 marks]
(k+20−2)=−23, k=−23 or y=−23x+c, c=−23∴ (M1)(A1)(ft)
Allow (0, - \frac{2}{3})
(M1) is for equating gradients or substituting gradient into y = mx + c (C2)
[2 marks]
Examiners report
There were some good answers, but many candidates showed a shaky understanding of coordinate geometry and some difficulty in dealing with negative numbers. Evidently a favourite question for some centres that consistently scored high marks here.
a) This was done quite well by most candidates with the main errors being reversal of the x, y values in the formula and using the negative, rather than the negative reciprocal for the perpendicular.
There were some good answers, but many candidates showed a shaky understanding of coordinate geometry and some difficulty in dealing with negative numbers. Evidently a favourite question for some centres that consistently scored high marks here.
b) Poorly answered though many candidates did gain a mark by substituting the correct value for gradient into y = mx + c.