O-LevelMathematicsCoordinate geometry4024/22 · May/June 2022 · Q1012 Marks
D is the point (4, 6) and E is the point (e, e).
- (a)The length of DE is √20. Form an equation in e and solve it to find the possible coordinates of E. Show your working.[5]
- (b)(i)F is the point (–f, 5f). The gradient of the perpendicular bisector of DF is 3/2. Find the value of f.[4]
- (b)(ii)The equation of the perpendicular bisector of DF is 2y = 3x+k. Find the value of k.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [5] M1 for (e-6)² + (e-4)² oe or √(e-6)²+(e-4)² ое A2 A1 for e² – 6e - 6e + 36 oe or e²-4e-4e + 16 oe M1 FT for factorising or correct use of formula for their 3-term quadratic B1 for (2, 2) and (8, 8)
- [4] B1 for [grad perpendicular =] -2/3 soi M2 for (5f-6)/(-f-4) = their (-2/3) oe or M1 for (5f-6)/(-f-4) oe or 6 = their (-2/3) x 4 + c oe
- [3] M1 for (4+(-theirf))/2 , (6+(5xtheirf))/2 M1 for substituting their (1, 8) into 2y = 3x + k oe
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