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Question

Question 7 (ii)
Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC.

(b) Find the coordinates of the point P on AD such that AP : PD = 2 : 1.

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Solution

(b) Coordinates of P can be calculated as follows using section formula:

x=m1x2+m2x1m1+m2,y=m1y2+m2y1m1+m2
In this case (m1=1,m2=2 and x1=4,x2=72,y1=2,y2=92)
x=1×4+2×723
=4+73=113
y=1×2+2×923
=2+93=113
Therefore, coordinates of point P are (113,113)

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