Question

Find the correct option regarding given points $(1,2),(2,4)$ and $(3,6)$

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

Answer 1

Answer: (C)

Collinear

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

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

Here the points are $(1,2)$, $(2,4)$ and $(3,6)$, therefore, the area of the triangle is:

$A=\frac{1}{2}\left|x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right|A=\frac{1}{2}\left|1\right(4-6)+2(6-2)+3(2-4\left)\right|\Rightarrow A=\frac{1}{2}\left|1\right(-2)+2(4)+3(-2\left)\right|\Rightarrow A=\frac{1}{2}|-2+8-6|\Rightarrow A=\frac{1}{2}|-8+8|\Rightarrow A=0$

Since the area of the triangle is zero,

Hence, the points are collinear.