Question

Area of the triangle with vertices A(5,2) B(4,7) and C(7,-4) =

• A. -2 square units
• B. 2 square units
• C. 4 square units

Answer 1

The correct option is B 2 square units

Area of the triangle with vertices A$(x_1,y_1)$, B$(x_2,y_3)$ and C$(x_3,y_3)$ = $\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$ = $\frac{1}{2}\left[5\right(7+4)+4(-4-2)+7(2-7\left)\right]$ = $\frac{1}{2}\times (55-24-35)=-2$

Since area is a measure, which cannot be negative, we will take the numerical value of -2, ie. 2.
$\therefore$ The area of the triangle = 2 square units.