Question

If three points $(h,0),(a,b)$ and $(0,k)$ tie on a line, show that $\frac{a}{h}+\frac{b}{k}=1$.

Answer 1

$(h,0),(a,b),(0,k)$ lie in the same line so

$\frac{h-a}{0-b}=\frac{a-0}{b-k}(h-1)(b-k)=-abbh-hk-ab+ak=-abbh+ak=hk$

$\frac{bh}{hk}+\frac{ak}{hk}=1,\frac{a}{h}+bk=1,\frac{a}{h}+\frac{b}{k}=1$