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in Coordinate Geometry by (29.9k points)
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The line 2x + y - 4 = 0 divide the line segment joining A(2,-2) and B(3,7) in the ratio 

(a) 2:5 

(b) 2:9 

(c) 2:7 

(d) 2:3

1 Answer

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Best answer

Correct answer is (b) 2:9

Let the line 2x + y - 4 = 0 divide the line segment in the ratio k :1 at the point P.

Then, by section formula the coordinates of Pare

\(P(\frac{3k\,+\,2}{k\,+\,1},\frac{7k\,-\,2}{k\,+\,1})\)

Since P lies on the line 2x + y - 4 = 0, we have

Hence, the required ratio is \(\frac{2}{9}:1\) which is same as 2 : 9.

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