The point P lies on the line joining A(-2, 3) and B(10,19) such that AP:PB = 1:3.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

1. [1] B1 for convincing argument for x = 1 (AB = (12, 16), at P, x = -2 + 1/4(12) so at P, x=1)
2. [1] B1 for y = 7 (y = 3 + 1/4(16), y = 7)
3. [1] M1 for finding gradient of perpendicular (Gradient of AB = 16/12, so perp gradient = -3/4)
4. [1] M1 for equation of perpendicular through their P (Perp line: y-7 = -3/4(x-1))
5. [1] A1 Allow unsimplified (3x+4y = 31)
6. [1] B1 ft ft on their perpendicular line, may be implied (Q = (0, 31/4))
7. [1] M1 for any valid method of finding the area of the correct triangle, allow use of their Q; must be in the form (0,q).
8. [1] A1 Area AQB = 12.5