Question

If $P(x,y)$ is any point on the line segment joining the points $(a,0)$ and $(0,b)$ then prove that $\frac{x}{a}+\frac{y}{b}=1$

Answer 1

Now the points $(x,y),(a,0)$ and $(0,b)$ are collinear.
$\therefore$ The area of the triangle formed by them is zero.
$\Rightarrow$ $ab-bx-ay=0$
$\therefore$ $bx+ay=ab$
Dividing by $ab$ on both sides, we get
$\frac{x}{a}+\frac{y}{b}=1$, where $a,b\ne 0$