8 A is the point (−2, 3) and B is the point (4, 5). (a) Find the coordinates of the midpoint of AB. (b) Show that the equation of line AB is 3y = x+11. (c) Find the equation of the perpendicular bisector of line AB.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

1. [1] (a) (1, 4)
2. [3] (b) Gradient = (5-3)/(4--2) oe
3. [3] M1
4. [3] 5 = (their 1/3) × 4 + c oe
5. [3] M1 (4, 5), (-2, 3) or their midpoint substituted into y = (their 1/3) x + c oe
6. [3] Rearrangement to c = 11/3 and hence showing 3y = x + 11
7. [3] A1 or expansion to 3y – 15 = x – 4 with completion or expansion to 3y – 9 = x + 2 with completion or expansion to 3y – 12 = x – 1 with completion With no errors or omissions in working
8. [3] (c) y = -3x + 7
9. [3] B1FT for gradient = -1 / their (b) gradient
10. [3] M1 for substituting their (1, 4) into y = their (-3)x + c oe