Prove the following

Solution:

D. (– 1, –1)

Explanation:

Given points are $(2,-3)$ and $(4,-5)$ Firstly,

we find the equation of line.

We know that,

Equation of line when two points are given:

$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\left(x-x_{1}\right)$

Putting the values, we get

$y-(-3)=\frac{-5-(-3)}{4-2}(x-2)$

$\Rightarrow y+3=\frac{-5+3}{2}(x-2)$

$\Rightarrow y+3=\frac{-2}{2}(x-2)$

$\Rightarrow y+3=-1(x-2)$

$\Rightarrow y+3=-x+2$

$\Rightarrow x+y=2-3$

$\Rightarrow x+y=-1$

$\Rightarrow \frac{x}{-1}+\frac{y}{-1}=1$ (Intercept form)

Comparing the above equation with the given equation $\frac{x}{a}+\frac{y}{b}=1$, we get the

value of $a$ and $b$

$a=-1$ and $b=-1$

 

Hence, the correct option is (d)