Question

Find the area of the triangle formed by the coordinates axes and the line $ax+by=2ab$.

Answer 1

$ax+by=2ab=>\frac{ax}{2ab}+\frac{by}{2ab}=1=>\frac{x}{2b}+\frac{y}{2a}=1$

So the vertices of the triangle are $(0,0),(0,2a),(2b,0)$

Therefore, area of the triangle is $\frac{1}{2}\times 2b\times 2a=2ab$