Question

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

• 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 $(2,2)$, $(1,2)$ and $(3,1)$, therefore the area of the triangle is:

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

Since the area of the triangle is not zero,

Hence, the points are non-collinear.