Question

If the vertices of a triangle are $(1,2),(4,-6)$ and $(3,5)$, then its area is

• A. $\frac{23}{2}$ sq. units
• B. $\frac{25}{2}$ sq. units
• C. $12$ sq.unit
• D. none of these

Answer 1

The correct option is B $\frac{25}{2}$ sq. units

Area of triangle having vertices $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ is given by
Area $=\frac{1}{2}\times \left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

Therefore, area of required triangle is given by

Area $=\frac{1}{2}\times \left[1\right(-6-5)+4(5-2)+3(2+6\left)\right]$

$=\frac{1}{2}[-11+12+24]$

$=\frac{1}{2}\times 25$

$=\frac{25}{2}sq.unit$