Relative Position of a Point with Respect to a Line
Question 7 ii...
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=2andx1=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)