Question

What is the sum of the length of intercepts made by the line joining the points $(4,5)$ and $(1,2)$ with $x$ and $y$ axis.

Answer 1

Equation of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

so the equation of the given line passing through $(4,5)$ and $(1,2)$ is

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

$y-5=x-4$

$x-y=-1$

Convert the above equation into the intercept form of line $\frac{x}{a}+\frac{y}{b}=1$

That is,

$\frac{x}{-1}+\frac{y}{1}=1$

So, the sum of length of the intercepts on the axis is $=1+1=2$