O-LevelAdditional MathematicsStraight line graphs4037/21 · Oct/Nov 2010 · Q109 Marks
Solutions to this question by accurate drawing will not be accepted. The diagram shows a quadrilateral ABCD in which A is the point (1, 4) and B is the point (6, 5). Angle ABC is a right angle and the point C lies on the x-axis. The line AD is parallel to the y-axis and the line CD is parallel to BA. Find
- (i)the equation of the line CD,[5]
- (ii)the area of the quadrilateral ABCD.[4]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.
- [B1] (i) m_AB = 1/5
- [M1] (i) Use m₁m₂ = -1 in equation for BC [y – 5 = –5(x – 6) or 5x + y = 35]
- [A1] (i) C (7,0)
- [M1] (i) Use m_CD = m_AB and point C in equation of line
- [A1] (i) CD: y – 0 = 1/5 (x – 7) or x – 5y = 7
- [M1] (ii) At D x = 1
- [A1] (ii) At D y = -1.2
- [M1] (ii) Method for area not involving measuring
- [A1] (ii) 28.6
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