If three points $(h, 0)$, $(a, b)$, and $(0, k)$ are collinear, then which of the following relations is true?
1 mark
🔍 View Detailed Solution & Schema →

Question

If three points $(h, 0)$, $(a, b)$, and $(0, k)$ are collinear, then which of the following relations is true?

Accepted Answer

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.

Straight Lines

❓ Sibling Questions in this Chapter