A-LevelMathematicsCoordinate geometry9709/12 · Oct/Nov 2011 · Q99 Marks
The diagram shows a quadrilateral ABCD in which the point A is (-1, -1), the point B is (3, 6) and the point C is (9, 4). The diagonals AC and BD intersect at M. Angle BMA = 90° and BM = MD. Calculate
- (i)the coordinates of M and D,[7]
- (ii)the ratio AM : MC.[2]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [7] Gradient of AC = ½
- [7] Gradient of BD = -2
- [7] Eqn of BD is y – 6 = -2(x - 3)
- [7] Eqn of AC is y + 1 = ½ (x + 1)
- [7] → M (5,2)
- [7] → D (7,-2)
- [2] Ratio of AM : MC = √45 : √20
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