Question

The graphing troubles me

Answer 1

The vertices are given as D(-8,4), E(-2,2), and F(-5,9).

Consider that area of the traingle is given by,

`\text{Area}=(1)/(2)\lbrack x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\rbrack`

Then the area of triangle DEF is given by,

`\text{Area}=(1)/(2)\lbrack-8(2-9)-2(9-4)-5_{}(4-2)\rbrack=(1)/(2)\lbrack-8(-7)-2(5)-5(2)\rbrack`

Simplify the terms further as,

`\text{Area}=(1)/(2)\lbrack56-10-10\rbrack=(1)/(2)(36)=18`

Thus, the area of the triangle is 18 square units.