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Further Mathematics Paper 2, May/June. 2009  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength



Question 7

The coordinates of the vertices of triangle ABC are A(-2, 1), B(4, -2) and C(1,8) respectively.  If D(x, y) is the foot of the perpendicular from A to BC, find

(a)      an equation connecting x and y
(b)     the unit vector in the direction of BC.

_____________________________________________________________________________________________________
Observation

For a clearer understanding of what is to be done, candidates were expected to sketch the diagram first.

From the diagram, gradient of BC =8+2/1-4 = -10/3 Gradient of AD = y-1/x+2. Since they are perpendicular, y-1/x+2 * -10/3 = -1 then 10y - 10 = 3x + 6  ; 10y – 3x - 16 = 0.
In part (b), length of BC = √ (8 + 2)2+ (1 - 4)2 =   √109.  The unit vector is obtained by:

 (-3i + 10j) = √109 (-3i + 10j)
    √109           109 

The Chief Examiner reported that this question was not attempted by majority of the candidates.  Some of those who attempted it displayed poor knowledge of the principle of perpendicularity of lines.  Hence could not obtain the correct equation. 

In part (b), although candidates displayed a good knowledge of the concept of unit vectors, many of them could not obtain the correct answer because they could not get the correct vector.
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