Question

If the points (a, 0), (0, b) and (1, 1) are collinear then which of the following is true ?

• A. $\frac{1}{a}+\frac{1}{b}=1$
• B. $\frac{1}{a}-\frac{1}{b}=2$
• C. $\frac{1}{a}-\frac{1}{b}=-1$
• D. $\frac{1}{a}+\frac{1}{b}=2$

Answer 1

The correct option is A $\frac{1}{a}+\frac{1}{b}=1$

Given that three points are collinear, $(a,o),(o,b)$ and $(1,1)$

Since the points are collinear, area of triangle formed by these points is equal to O.

$\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]=0\frac{1}{2}[a[b-1]+0[1-0]+1(0-b\left)\right]=0\Rightarrow ab-a-b=0\Rightarrow a+b=ab\therefore \frac{1}{a}+\frac{1}{b}=1$