Question

Find the correct option regarding the given points $(2,-1),(0,2)$ and $(3,2)$.

• A. Collinear
• B. Non-collinear
• C. Exists on parallel lines
• D. Exists on perpendicular lines

Answer 1

The correct option is B Non-collinear

Area of the triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$ is:

$A=\frac{1}{2}\left|x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right|$

Here the points are $(2,-1)$, $(0,2)$ and $(3,2)$, therefore, the area of the triangle is:

$A=\frac{1}{2}\left|2\right(2-2)+0(2+1)+3(-1-2\left)\right|\Rightarrow A=\frac{1}{2}\left|2\right(0)+0(3)+3(-3\left)\right|\Rightarrow A=\frac{1}{2}|-9|\Rightarrow A=\frac{9}{2}\ne 0$

Since the area of the triangle is not zero,

Hence, the points are non-collinear.