MP Board · Class 11 · Mathematics · Straight LinesIf three points $(h, 0)$, $(a, b)$, and $(0, k)$ are collinear, then which of the following relations is true?

If three points are collinear, the slope of the line segment joining the first two points is equal to the slope of the line segment joining the last two points. Slope between $(h, 0)$ and $(a, b)$ is $\frac{b - 0}{a - h}$. Slope between $(a, b)$ and $(0, k)$ is $\frac{k - b}{0 - a}$. Equating them: $\frac{b}{a - h} = \frac{k - b}{-a} \implies -ab = (k - b)(a - h) \implies -ab = ak - ah - ab + bh \implies ah + bk = ab$. Dividing by $ab$, we get $\frac{h}{a} + \frac{k}{b} = 1$. Therefore, the correct option is C.