A is the point (3, 11) and B is the point (-5, -5). The equation of line L is 2y+x = 5. Show that line L is the perpendicular bisector of AB.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. 24 [Midpoint of AB =] (-1, 3)
2. 24 11 - (-5) / 3 - (-5) oe
3. 24 [Gradient of AB =] 2 and [Gradient of perpendicular = ] -1/2 soi
4. 24 EITHER Method 1: 2x3 + -1 = 5
5. 24 Or substitution of x = -1 or y = 3 into 2y+x=5 to evaluate corresponding y or x
6. 24 States (-1, 3) is on L oe and gradient L = -1/gradient AB oe
7. 24 OR Method 2: substitution of (-1, 3) into y = -1/2 x + c oe
8. 24 or substitution of (-1, 3) into y-y1 = -1/2 (x-x1)
9. 24 correct rearrangement to 2y + x = 5
10. 24 or c = 5/2 oe and rearrangement of L to y = -1/2 x + 5/2