Question

The area of a triangle with the vertices $(1,2),(3,4)$ and $(5,6)$, is ____ square units.

• A. $0$
• B. $1$
• C. $2$
• D. $5$

Answer 1

Answer: (A)

$0$

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

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

Therefore, the area of triangle with vertices $(1,2)$, $(3,4)$ and $(5,6)$ is:

$A=\frac{1}{2}\left|2\right(3-5)+4(5-1)+6(1-3\left)\right|=\frac{1}{2}|-4+16-12|=\frac{1}{2}|16-16|=\frac{1}{2}\left|0\right|=0$

Hence, the area of the triangle is $0$.