Question

determine the ratio in which line 2x+y-4=0 divides the joining of (-2,2) , (3,7)

Answer 1

Heya,

Let the line divided it in the ratio k : 1 .

Thus, by section formula,

Coordinate of the point which divides it in the ratio k : 1 is $x = \frac{3k - 2}{k + 1} \:and \: y = \frac{7k + 2}{k + 1}$

Now, this point will lies on the given line :-

$2( \frac{3k - 2}{k + 1} )\: + \: ( \frac{7k + 2}{k + 1} ) - 4 = 0$

Solving it, we get

K = $\frac{2}{9}$

So, ratio= K:1, i.e

$\frac{2}{9}$ Ans.

Thanks

KSHITIJ