O-LevelAdditional MathematicsStraight line graphs4037/21 · May/June 2014 · Q98 Marks
Solutions to this question by accurate drawing will not be accepted. The points A(p,1), B(1, 6), C(4, q) and D(5, 4), where p and q are constants, are the vertices of a kite ABCD. The diagonals of the kite, AC and BD, intersect at the point E. The line AC is the perpendicular bisector of BD. Find
- (i)the coordinates of E,[2]
- (ii)the equation of the diagonal AC,[3]
- (iii)the area of the kite ABCD.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.
- [B1B1] (3, 5) column vector B0B1
- [M1] m_BD = (6-4)/(1-5) = -1/2 can be implied by second M1
- [M1] m_AC = -1 ÷ (-1/2) seen or used
- [A1] y – 5 = 2(x - 3) or y = 2x + c, c = −1 or better
- [M1] p=1 q=7 [A(1, 1) C(4, 7)] could be in (ii)
- [M1] Method for finding area numerically e.g. 24 - (1/2 × 1 × 3 + 1/2 × 1 × 3 + 1/2 × 1 × 4)
- [A1] 15 or shoelace method SC2 for 15 with no working
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