Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js

User interface language: English | Español

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.

[4]
a.

The perpendicular line drawn through M meets the y-axis at R (0, k).

Find k.

[2]
b.

Markscheme

(i) (2, – 2) parentheses not required.     (A1)

 

(ii) gradient of PQ =(5104)=64=32(1.5)     (M1)(A1)

(M1) for gradient formula with correct substitution

Award (A1) for y=32x5 with no other working

(iii) gradient of perpendicular is 23     (A1)(ft)     (C4)

 

[4 marks]

a.

(k+202)=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]

b.

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.

 

a.

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.

b.

Syllabus sections

Topic 5 - Geometry and trigonometry » 5.1 » Gradient; intercepts.
Show 55 related questions

View options