Question

Find the area of the triangle whose vertices are (4, -3), (-9, 7) and (8, 8).

Answer 1

Area of triangle \(=\frac{1}{2}\left[x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)\right]\)

\( \begin{aligned} & =\frac{1}{2}[4(7-8)+(-9)(8-(-3)+8(-3-7)] \\ & =\frac{1}{2}[4(-1)+(-9)(11)+8(-10)] \\ & =\frac{1}{2}[-4-99-80] \\ \end{aligned} \)

\(=\frac{1}{2} \times 183=91.5 \) sq. units