Question

Triangle DEF has vertices D = (-4,-4), E = (-2,-4), and F = (-3,-1). 5! 3 2 1 -7 6 5 4 3 2 2 3 4 5 6 10 5 3. What is the area of the triangle? Show your reasoning. 1. Plot the triangle in the coordinate plane and label the vertices. 2. Name the coordinates of 3 points that are inside the triangle.

please help !!! <3​

Answer 1

`Area = 3`

Explanation:

Given

`D = (-4,-4)`

`E = (-2,-4)`

`F = (-3,-1)`

Solving (a) and (b):

See attachment for plot and labelled vertices

Solving (c): The area

This is calculated using:

`Area = (1)/(2)|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2+x_3y_1 - x_1y_3|`

Where:

`D = (-4,-4)` --
`(x_1,y_1)`

`E = (-2,-4)` --
`(x_2,y_2)`

`F = (-3,-1)` --
`(x_3,y_3)`

This gives:

`Area = (1)/(2)|(-4*-4) - (-4*-2) + (-2 *-1) - (-3*-4)+(-3*-4) - (-4*-1)|`

`Area = (1)/(2)|16 - 8 +2- 12+12 - 4|`

`Area = (1)/(2)|6|`

This gives

`Area = (1)/(2) * 6`

`Area = 3`