Question

Prove that the points whose coordinates are respectively $(5,1),(1,-1)$, and $(11,4)$ lie on a straight line, and find its intercepts on the axes.

Answer 1

Given: Equation of line joining $(5,1)\equiv (x_1,y_1)$ and $(1,-1)\equiv (x_2,y_2)$ is

$y-y_1=m(x-x_1)$

$m=\left(\frac{y_2-y_1}{x_2-x_1}\right)$

$y-1=\left(\frac{-1-1}{1-5}\right)(x-5)$

$y-1=\frac{2}{4}(x-5)$

$4y-4=2x-10$

$2x-4y=6$

$x-2y=\mathrm{3.......}\left(i\right)$

Substituing $(11,4)$ in $\left(i\right)$

$\left(11\right)-2\left(4\right)=3$

$11-8=3$

$3=3$

It satisfies the equation of line, so all the points lie on the same straight line.

$x-2y=3x=0\Rightarrow y=-\frac{6}{4}=-\frac{3}{2}y=0\Rightarrow x=3$

So $x$ intercept is $3$ and $y$ intercept is $-\frac{3}{2}$