Question 12
- If x = , y = and z = , find scalars p and q such that px + qy = z.
- Using a scale of 2 cm to 2 units on both axes, draw on a graph paper two perpendicular axes 0x and 0y for respectively.
- Draw, on the same graph paper, indicating clearly the vertices and their coordinates,
- the quadrilateral WXYZ with W(2, 3), X(4, -1), Y(-3, -4) and Z(-3, 2);
- the image W1X1Y1Z1 of the quadrilateral WXYZ under an anticlockwise rotation of about the origin where W W1, X X1, Y Y1 and Z Z1.
Observation
The Chief Examiner reported that vectors was poorly attempted and completely avoided by majority of the Candidates’.
In part (a), they were expected to substitute and multiply the column vectors by p and q to get:
p
2p + 5q = – 4 ………………(1)
3p – 2q = 13………………..(2)
Solving equations (1) and (2) simultaneously, will gave q = –2 and p = 3.
In part (b), the graph for the quadrilateral WXYZ with W(2,3), X(4,-1), Y(-3,-4) and Z(-3,2) is as shown and for the image of the quadrilateral WXYZ under an anticlockwise rotation of , the vertices and the coordinates are W1(-3,2), X1(1,4), Y1(4, -3) and
Z1(-2,-3) .
