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Question

If Point P (-4,6) divides the line segment AB with A(-6,10) and B(x,y) in the ratio 3:2 internally, find the co-ordinates of B.

A
(113,143)
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B
(83,103)
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C
(83,103)
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D
(163,83)
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Solution

The correct option is C (83,103)
The equation for the point that divides a line segment joining the points (x1,y1) and (x2,y2) in the ratio m : n is: ((n×x1+m×x2)m+n,n×y1+m×y2m+n)

Here,
(x1,y1)=(6,10),(x2,y2)=(x,y), m:n=3:2
According to Section Formula:
(x,y)=(mx2+nx1m+n,my2+ny1m+n)
(4,6)=(3x+(12)3+2,3y+203+2)
4=3x125 and 6=3y+205
3x=20+12 and 3y=3020
x=83 and y=103
Co-ordinates of B are (83,103).

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