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

Answer:

$Area = 3$

Step-by-step 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:

$Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2+x_3y_1 - x_1y_3|$

Where:

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

$E = (-2,-4)$  -- $(x_2,y_2)$

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

This gives:

$Area = \frac{1}{2}|(-4*-4) - (-4*-2) + (-2 *-1) - (-3*-4)+(-3*-4) - (-4*-1)|$

$Area = \frac{1}{2}|16 - 8 +2- 12+12 - 4|$

$Area = \frac{1}{2}|6|$

This gives

$Area = \frac{1}{2} * 6$

$Area = 3$