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Question

The ratio in which the line 2x + y –4 = 0 divides the line segment joining the points A(2,–2) and
B(3, 7) is .

A
2:9
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B
9:2
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C
2:7
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D
7:2
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Solution

The correct option is A 2:9
Let the line 2x+y-4 = 0 intersects the line segment AB at point C and C divides AB in the ratio k : 1.
Coordinates of C will be
(3k+2k+1,7k2k+1)
Also, point C lies on the line 2x+y-4 = 0, so it must satisfy its equation.
2(3k+2k+1)+(7k2k+1)=46k+4+7k2k+1=413k+2=4k+49k=2k=29

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