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Codykrieger · Answer 1 · 2023-09-11T12:55:44+0000

The triangle ΔDEF has the following coordinates

$\lbrace D(-1,6),E(-4,-6),F(3,-5)\rbrace$

To find the area of a triangle in coordinate geometry, we have a formula. Given 3 vertices A(x1, y1), B(x2,y2) and C(x3,y3), the area of this triangle is given by

$Area(\Delta ABC)=(1)/(2)|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

Using this formula for our problem, we have

$Area_(\Delta DEF)=(1)/(2)|(-1)((-6)-(-5))+(-4)((-5)-6)+3(6_{}-(-6))|$

Solving this equation, we have

$\begin{gathered} Area_(\Delta DEF)=(1)/(2)|(-1)((-6)-(-5))+(-4)((-5)-6)+3(6_{}-(-6))| \\ =(1)/(2)|(-1)((-6+5)+(-4)(-5-6)+3(6_{}+6)| \\ =(1)/(2)|(-1)(-1)+(-4)(-11)+3(12)| \\ =(1)/(2)|1+44+36| \\ =(1)/(2)|81| \\ =(81)/(2) \\ =40.5 \end{gathered}$

And this is our answer Area(ΔDEF) = 40.5

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