Question

Let the algebraic sum of the perpendicular distance from the points $(2,0)(0,2)$ and $(1,1)$ to a variable straigth line be zero, then the passes through a fixed point whose coordinates are........ Find the condition on $a$ and $b$, such that the portion of theline$ax+by-1=0$, intercepted between the line axis.

Answer 1

$variable0fax+by+c=0$

$algebricsumofperpendicular\left(20\right)\left(02\right)\left(11\right)$

$\left[\frac{2\times a+b\times 0+c}{\sqrt{a^2+b^2}}\right]+\left[\frac{a\times 0+b\times 2+c}{\sqrt{a^2+b^2}}\right]+\left[\frac{a\times 1+b\times 1+c}{\sqrt{a^2+b^2}}\right]$

$\pm \left(\frac{2a+c}{\sqrt{a^2+b^2}}\right)\pm \left(\frac{2b+c}{\sqrt{a^2+b^2}}\right)\pm \left(\frac{a+b+c}{\sqrt{a^2+b^2}}\right)$

$2a+c+2b+c+a+b+c=0$

$3a+3b+3c=0$

$a+b+c=0$