Answer to Question #160324 in Analytic Geometry for Viktoriya

Question

find the area of a triangle with vertices E(1,3) F(-4,-3) G(5,-4)

Answer 1

Require to find the area of the triangle: $E(1,3),F(-4,-3),G(5,-4)$

Let $(x_{1},y_{1})=(1,3),(x_{2},y_{2})=(-4,-3),(x_{3},y_{3})=(5,-4)$

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

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

$=\frac{1}{2}\left [ 1+28+30 \right ] =\frac{59}{2}$ square units