Solutions to this question by accurate drawing will not be accepted. The points A(-3, 2) and B(1, 4) are vertices of an isosceles triangle ABC, where angle B = 90°.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.

1. [B1] (i) √20 or 4.47
2. [M1] (ii) for attempt at a perp gradient
3. [M1, A1] for attempt at straight line equation, must be perpendicular and passing through B.
4. [A1] allow unsimplified (y = -2x + 6)
5. [M1] (iii) for attempt to obtain relationship using an appropriate length and the point (1, 4) or (-3, 2) (e.g. BC²=20 or AC²=40)
6. [A1] for a correct equation
7. [DM1] for attempt to solve with y = -2x + 6 and obtain a quadratic equation in terms of one variable only
8. [DM1] for attempt to solve quadratic
9. [A1, A1] for each 'pair' (x = 3, -1 and y = 0, 8)
10. Or, using vector approach:
11. [B1] (AB = (4 2)) May be implied
12. [M1] for correct approach (OC = OB + BC)
13. [A1, A1] for each element correct
14. [A1, A1] for each element correct