Question

If the points $(a,0)(0,b)$ and $(1,1)$ are col linear ,show that

$\frac{1}{a}+\frac{1}{b}=1$

• A. $-3$
• B. $1$
• C. $-14$
• D. $-7$

Answer 1

Answer: (B)

$1$

$\begin{array}{c}\left(a,0\right)\left(0,b\right)\left(1,1\right)\\ =\frac{1}{2}\left[a\left(b-1\right)+0\left(1-0\right)+1\left(0-b\right)\right]\\ =\frac{1}{2}\left[ab-a-b\right]=0\\ ab-a-b=0\\ a+b=ab\end{array}$

Dividing both sides by $ab$

$\begin{array}{c}\frac{a}{ab}+\frac{b}{ab}=\frac{ab}{ab}\\ \frac{a}{ab}+\frac{b}{ab}=1\\ \frac{1}{b}+\frac{1}{a}=1\end{array}$