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3 February, 00:04

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.

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  1. 3 February, 00:05
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    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.
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