CBSE · Class 10 · Mathematics · Coordinate GeometryIf the points $(1, 2)$, $(0, 0)$ and $(a, b)$ are collinear, then which of the following is true?
For points to be collinear, the area of the triangle formed by them must be 0. Alternatively, the slope of the line joining $(1, 2)$ and $(0, 0)$ must equal the slope of the line joining $(0, 0)$ and $(a, b)$. Slope = $\frac{2 - 0}{1 - 0} = 2$. Slope with $(a, b)$ is $\frac{b - 0}{a - 0} = \frac{b}{a}$. Thus, $\frac{b}{a} = 2 \implies b = 2a$. Therefore, the correct option is C.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Coordinate Geometry.
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Coordinate Geometry.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Coordinate Geometry.