O-LevelAdditional MathematicsStraight line graphs4037/11 · May/June 2016 · Q810 Marks
Solutions to this question by accurate drawing will not be accepted. Three points have coordinates A(-8, 6), B(4, 2) and C(-1, 7) . The line through C perpendicular to AB intersects AB at the point P.
- (i)Find the equation of the line AB.[2]
- (ii)Find the equation of the line CP.[2]
- (iii)Show that P is the midpoint of AB.[3]
- (iv)Calculate the length of CP.[1]
- (v)Hence find the area of the triangle ABC.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [1] Gradient of AB = (2-6)/(4-(-8)) = -1/3
- [1] y - 6 = -1/3 (x + 8) or 3y + x = 10
- [1] Gradient of CP = 3
- [1] y - 7 = 3 (x + 1) or y = 3x + 10
- [1] Point of intersection (-2, 4)
- [1] Midpoint of AB = ((-8+4)/2, (6+2)/2) = (-2, 4)
- [1] P is the midpoint of AB
- [1] CP = √(( -2 - (-1))^2 + (4 - 7)^2) = √10 or 3.16
- [1] Length of AB = √((4 - (-8))^2 + (2 - 6)^2) = √160 = 4√10
- [1] Area = 1/2 * √160 * √10 = 20
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