O-LevelAdditional MathematicsStraight line graphs4037/22 · Oct/Nov 2015 · Q810 Marks

Solutions to this question by accurate drawing will not be accepted. Two points A and B have coordinates (–3, 2) and (9, 8) respectively.

(i)Find the coordinates of C, the point where the line AB cuts the y-axis.[3]
(ii)Find the coordinates of D, the mid-point of AB.[1]
(iii)Find the equation of the perpendicular bisector of AB.[2]
(iv)The perpendicular bisector of AB cuts the y-axis at the point E. Find the coordinates of E.[1]
(v)Show that the area of triangle ABE is four times the area of triangle ECD.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.

[B1] (i) Gradient AB = (8-2)/(9+3) = 6/12 = 1/2 isw
[M1] (i) Equation AB and x=0 → (y-2)/(0+3) = 1/2 → y = 3.5 Find equation with their gradient and set x = 0
[A1] (i)
[B1] (ii) D is (3, 5)
[M1] (iii) Gradient perpendicular = -2 Use of m₁ × m₂ = −1 on gradient used for their line in (i)
[A1] (iii) Equation perpendicular (y-5)/(x-3) = -2 → (y = -2x+11)
[A1FT] (iv) E is (0, 11)
[M1] (v) Area of ABE = 1/2 | -3 9 0 -3 / 2 8 11 2 | For area of ABE or ECD. 1/2 and their correct 8 elements must be seen.
[A1] (v) = 1/2 |-24 + 99 - 18 + 33| = 45 45 condone from E (0, -4)
[A1] (v) Area of EDC = 1/2 | 0 3 0 0 / 3.5 5 11 3.5 | = 1/2 |-10.5+33|=11.25 11.25 condone from E(0, -4)

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