O-LevelAdditional MathematicsStraight line graphs4037/22 · Oct/Nov 2020 · Q38 Marks
Find the equation of the perpendicular bisector of the line joining the points (12, 1) and (4, 3), giving your answer in the form y = mx+c.
- (a)Find the equation of the perpendicular bisector of the line joining the points (12, 1) and (4, 3), giving your answer in the form y = mx+c.[5]
- (b)The perpendicular bisector cuts the axes at points A and B. Find the length of AB.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [B1] (a) Gradient of line = (3-1) / (4-12)
- [M1] (a) Gradient of perpendicular = 4 -1 / their grad line
- [B1] (a) Mid-point is (8, 2)
- [M1] (a) Equation: (y-2) / (x-8) = 4 Using their perpendicular gradient and mid-point
- [A1] (a) y = 4x - 30
- [B1] (b) x = 0 → (y) = -30 FT equation must have 3 terms
- [B1] (b) y = 0 → (x) = 7.5 FT equation must have 3 terms
- [B1] (b) AB = √30^2 + 7.5^2 = 30.9 or better nfww Accept exact answer of 15√17 / 2
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