A-LevelMathematicsCoordinate geometry9709/12 · Oct/Nov 2022 · Q16 Marks
Points A and B have coordinates (5, 2) and (10, −1) respectively.
- (a)Find the equation of the perpendicular bisector of AВ.[3]
- (b)Find the equation of the circle with centre A which passes through B.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- B1 Accept unsimplified. Mid-point AB is ( (10+5)/2 , (2-1)/2 ) or (15/2, 1/2)
- M1 For use of (Change in y)/(Change in x) , condone inconsistent order of x and y, and m₁m₂ = -1. Gradient of AB = (-1-2)/(10-5) = -3/5. Gradient perpendicular = 5/3
- A1 OE ISW. Any correct version e.g. y-1/2 = 5/3(x-15/2) or 5x-3y = 36.
- B1 Sight of √34 or 34. Condone confusion of r and r². [Radius =] √34 or 5.8 AWRT or [(radius)² =] 34
- B1 Sight of (x-5)²+(y-2)²
- B1 CAO ISW. (x-5)²+(y-2)² = 34
- B1 x² + y² - 10x – 4y
- B1 Substitution of (10, -1) into x² + y² −10x – 4y + c = 0. [c=]5or[c=]-5
- B1 x² + y² - 10x – 4y - 5 = 0
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