Maths / Coordinate Geometry / Section Formula

QUESTION

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

EXPLANATION
Explain TypeExplanation Content
Text

Suppose the line 2x+y-4=0 divides the line segment joining A(2,-2) and B(3,7) in the ratio K:1 at point C.

Then , the coordinates  of C are $\left ( \frac{3k+2}{k+1},\frac{7k-2}{k+1} \right )$

Angle required.

But C lies on 2x+y-4=0, therefore ,

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

$\Rightarrow 6k+4+7k-2-4k-4=0$

$\Rightarrow 9k-2=0$

$\Rightarrow 9k=2\Rightarrow \frac{2}{9}$

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