O-LevelMathematicsCoordinate geometry4024/22 · Oct/Nov 2023 · Q710 Marks

[Figure Cartesian Grid with points A and B]

(a)(i)ABC is a triangle. Here are five possible coordinates for point C. (-2, 4) (-2,-1) (-1,-2) (6, 1) (-4, 6) Tick (✔) the two coordinates from the list that make ABC an isosceles triangle.[2]
(a)(ii)Find the column vector AB .[1]
(a)(iii)A is the midpoint of the line DB. Find DB.[3]
(b)The equation of line P is y = 4x -3 . Line L is perpendicular to line P. Line L passes through the point (6, 4). Find the coordinates of the point where line L crosses the x-axis.[4]

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Mark scheme

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

[2] B1 for each
[1] (5, 3)
[3] M2 for (2×their 5)² +(2×their 3)² oe
or 2 sqrt((their 5)² +(their 3)²) oe
or M1 for [DB=](2xtheir 5, 2xtheir 3) or for (their 5)² +(their 3)² oe
After 0 scored, SC1 for (–9, -2) seen
[4] B1 for gradient = -1/4 oe
M1 for substituting (6, 4) in y = (their (-1/4))x + c oe
M1 for substituting y = 0 in y = (their (-1/4))x + k, where k is numerical
If 0 scored, SC1 for answer (5,0)

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