The area of the triangle of 18.
The area of a triangle on a coordinate plane is given by the formula,
[tex]Area\ \triangle = \dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
where,
[tex](x_1, y_1)[/tex], [tex](x_2, y_2)[/tex], and [tex](x_3, y_3)[/tex] are the coordinates of the three points in the coordinate plane.
A(2, -1) = [tex](x_1, y_1)[/tex]
B(5, 6) = [tex](x_2, y_2)[/tex]
C(-1, 4) = [tex](x_3, y_3)[/tex]
[tex]Area\ \triangle = \dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
[tex]\begin{aligned}Area \triangle &= \dfrac{1}{2}\ |2[6-4]+5[4-(-1)]-1[-1-6]|\\\\& = \dfrac{1}{2}\ |2[2]+5[4+1]-1[-7]|\\\\& = \dfrac{1}{2}\ |2[2]+5[5]-1[-7]|\\\\& =\dfrac{1}{2}|4+25+7|\\\\& = \dfrac{1}{2}\times 36\\\\& = 18\end{aligned}[/tex]
Hence, the area of the triangle of 18.
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