Question

Equation of the line which join the origin and the point of trisection of the portion of the line $x+3y-12=0$ intercepted between the axes is :

• A. $x=6y$
• B. $x-5y=0$
• C. $3x-7y=0$
• D. $2x-5y=0$

Answer 1

The correct option is A $x=6y$

the equation of the line segment is $x+3y-12=0$

when $x=0,y=4$ and when $y=0,x=12$

therefore the line intersects the coordinate axes at $(0,4)$ and $(12,0)$

Point of trisection divides segment in $1:2$ ratio

So,let $P(x,y)$ be the point of trisection

by applying section formula,

$x=\frac{2\times 12+0}{3},y=\frac{2\times 0+4}{3}$

$x=8,y=\frac{4}{3}$

$P(8,\frac{4}{3})$

$x=8$ and $y=\frac{4}{3}$

the required line passes through point $P(8,\frac{4}{3})$ and the origin

hence,by using slope point form,

$\Rightarrow x=6y$ locus of P point.