O-LevelMathematicsCoordinate geometry4024/22 · May/June 2018 · Q1010 Marks
A is the point (−4, −1), B is the point (2, 2) and BC = (4, -8).
- (a)Find the coordinates of the midpoint of AB.[1]
- (b)Find the gradient of AB.[1]
- (c)Show that BC is perpendicular to AB.[2]
- (d)ABCD is a rectangle. Find the coordinates of point D.[2]
- (e)Calculate the perimeter of rectangle ABCD.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [1] (-1, 0.5) or (-1, 1/2) cao
- [1] 1/2 oe
- [2] M1 for [Gradient of BC =] -8/4
- A1 1/2 × -8/4 = -1 hence perpendicular
- Alternative 2: M1 for AB = (6,3) oe and AC = (10,-5) oe
- A1 for (4^2+8^2) + (6^2+3^2) = (10^2+5^2) hence perpendicular
- [2] B1 for one value correct
- or M1 for (-4 - (-8)) + (2 + 4) oe or (6 - 6) + (-3) oe
- [4] M3 for [2x]√3^2 +6^2 + √4^2 + (-8)^2 oe
- or M2 for √4^2 + (-8)^2 oe or √3^2 +6^2 oe
- or M1 for 4^2 + (-8)^2 oe or 3^2 + 6^2 oe
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