Question

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

• A. 1/a + 1/b = 2
• B. 1/a + 1/b = 1
• C. 1/a + 1/b = 0
• D. 1/a + 1/b = 4

Answer 1

The correct option is B

1/a + 1/b = 1

Area of the triangle = $\frac{1}{2}$ [ $x_1$($y_2$ - $y_3$) + $x_2$($y_3$ - $y_1$) + $x_3$($y_1$ - $y_2$)]
For 3 points to be collinear the area of the triangle should be zero:
$\frac{1}{2}\left[a\right(b-1)+1(0-b\left)\right]=0$
$ab=a+b$
$\frac{1}{a}$ + $\frac{1}{b}$ = 1