O-LevelMathematicsVectors and transformations4024/21 · Oct/Nov 2022 · Q69 Marks
The position vector of point A is (4, 7) and the position vector of point B is (9, 2).
- (a)(i)Find the column vector AB.[1]
- (a)(ii)Find |AB|.[2]
- (a)(iii)ABCD is a parallelogram with sides AB, BC, CD and DA. BC = (-4, 1). Find the coordinates of point C and point D.[2]
- (b)P is the point (r, 4) and Q is the point (t, u). The midpoint of line PQ is (1, 3). The gradient of line PQ is -1/4. Find the value of each of r, t and u.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [1] (a)(i) (5, -5)
- [2] (a)(ii) 7.07[1...]; M1 Correct use of Pythagoras using their AB or OB-OA
- [2] (a)(iii) [C = ] (5, 3) [D = ] (0, 8); B1 for each
- [4] (b) [r = ] -3 [t = ] 5 [u = ] 2; B1 for u = 2 M2 for two correct equations involving r and/ or t or M1 for one correct equation involving r and/ or t OR B1 for r=-3 M2 for two correct equations involving u and/ or t or M1 for one correct equation involving u and/ or t After 0 scored, SC1 for (u-4)/(t-r) = 1/4
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