Question

Area of triangle whose vertices are $(0,0),(2,3),(5,8)$ is ____ square units.

• A. $\frac{1}{2}$
• B. $1$
• C. $2$
• D. $\frac{3}{2}$

Answer 1

Answer: (A)

$\frac{1}{2}$

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:

$A=\frac{1}{2}\left|0\right(2-5)+3(5-0)+8(0-2\left)\right|=\frac{1}{2}|0+15-16|=\frac{1}{2}|-1|=\frac{1}{2}$

Hence, the area of the triangle is $\frac{1}{2}$ square units.