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Question

Find the ratio in which the line 2x+3y−5=0 divides the line segment joining the points A(8,-9) and B(2,1).
If the ratio is m:n, then, m = ___.

A
8
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B
1
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C
2
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D
6
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Solution

The correct option is A 8
Given, A= (8,-9) and B = (2,1).

Let, the ratio in which the point on the line 2x+3y5=0 divides AB be k:1

If the point on the line segment is taken as P, then P has the coordinates (8×1+2×kk+1,9×1+1×kk+1)

= (8+2kk+1,9+kk+1)

Now, this point lies on the line 2x+3y5=0

Hence,
2×8+2kk+1+3×9+kk+15=0

2(8+2k)+3(9+k)5(k+1)=0

(16+4k27+3k5k5=0

2k16=0.

k=8

k:1=m:n=8:1

m=8

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