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Question

In what ratio does the line x-y-2 = 0 divide the linesegment joining the points A(3, -1) and B(8, 9) ?


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Solution

Let the line xy2=0 divide the line segment joining the points A(3,-1) and B(8,9) in the ratio k:1 at P

Then, by section formula the coordinates of P are

x=(mx2+nx1m+n,y=my2+ny1m+n)

P = x=8k+3k+1,y=9k1k+1

Since, P lies on the line xy2=0, we have.

(8k+3k+1)(9k1k+1)2=0

8k+39k+12k2=0

8k9k2k+3+12=0

3k+2=0

3k=2

k=23

So, the required ratio is 23:1, which is equal to 2 : 3


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