Question

What is the area of this triangle? Enter your answer in the box. units² A triangle D E F is graphed on a coordinate plane. The horizontal x-axis ranges from negative 5 to 2 in increments of 1. The vertical y-axis ranges from negative 2 to 2 in increments of 1. The vertex labeled as D is located at beginning ordered pair negative 1 comma negative 2 ends ordered pair. The vertex labeled as E lies at beginning ordered pair negative 5 commas 2 end ordered pair. The vertex labeled as Flies at beginning ordered pair 2 commas 2 ends ordered pair.

Answer 1

Answer:

The area of the triangle is 16 unit²

Step-by-step explanation:

Area of a triangle given coordinates

D = (-1, -2)

E = (-5, 2)

F = (2, 2)

We note that the formula for finding the are triangle given the coordinates if presented as follows;

A = (x₁·y₂ + x₂·y₃ + x₃·y₁ - x₁·y₃ - x₂·y₁ - x₃·y₂)/2

Where:

D = (x₁, y₁)

F = (x₂, y₂)

E = (x₃, y₃)

Therefore;

x₁ = -1, y₁ = -2, x₂ = 2, y₂ = 2, x₃ = -5,  y₃ = 2

Which gives;

A = ((-1)*(-2) + 2*2 + (-5)*(-2) - (-1)*2 - 2*(-2) - (-5)*2)/2

A = ((-1)·(-2) + 2·2 + (-5)·(-2) - (-1)·2 - 2·(-2) - (-5)·2)/2 = 16

The area of the triangle = 16 unit².