Answer:
[tex]Area = 3[/tex]
Step-by-step explanation:
Given
[tex]D = (-4,-4)[/tex]
[tex]E = (-2,-4)[/tex]
[tex]F = (-3,-1)[/tex]
Solving (a) and (b):
See attachment for plot and labelled vertices
Solving (c): The area
This is calculated using:
[tex]Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2+x_3y_1 - x_1y_3|[/tex]
Where:
[tex]D = (-4,-4)[/tex] -- [tex](x_1,y_1)[/tex]
[tex]E = (-2,-4)[/tex] -- [tex](x_2,y_2)[/tex]
[tex]F = (-3,-1)[/tex] -- [tex](x_3,y_3)[/tex]
This gives:
[tex]Area = \frac{1}{2}|(-4*-4) - (-4*-2) + (-2 *-1) - (-3*-4)+(-3*-4) - (-4*-1)|[/tex]
[tex]Area = \frac{1}{2}|16 - 8 +2- 12+12 - 4|[/tex]
[tex]Area = \frac{1}{2}|6|[/tex]
This gives
[tex]Area = \frac{1}{2} * 6[/tex]
[tex]Area = 3[/tex]
