Question

Area of a triangle formed by the points A(5, 2), B(4, 7) and C(7, -4) is _____.

• A. 2 sq. units
• B. $2\sqrt{2}$ sq. units
• C. 4 sq. units
• D. $4\sqrt{2}$ sq. units

Answer 1

Answer: (A)

Area of a triangle ABC = $\frac{1}{2}\left|\right[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]|$

Substituting the given coordinates, we have

=$\frac{1}{2}[5(7+4))-(4+2)+7(2-7))]$

$=\frac{1}{2}\left(5\right(11)+4\times (-6)+7\times (-5\left)\right)$

$=\frac{1}{2}\left[\right(55)-(24)-(35\left)\right]$

$=\frac{1}{2}\times |-4|=2$ square units.