Find the area of the triangle whose vertices | vedclass

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(A) The area of a triangle with vertices $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ is given by the formula:Area $= \frac{1}{2} |x_1(y_2 - y_3) + x_2(

Vedclass · Accepted Answer

$10.5$ square units

Vedclass · Answer

(A) The area of a triangle with vertices $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ is given by the formula:Area $= \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$Given vertices are $(x_1, y_1) = (2, 3), (x_2, y_2) = (-1, 0),$ and $(x_3, y_3) = (2, -4)$.Substituting these values into the formula:Area $= \frac{1}{2} |2(0 - (-4)) + (-1)(-4 - 3) + 2(3 - 0)|$Area $= \frac{1}{2} |2(4) + (-1)(-7) + 2(3)|$Area $= \frac{1}{2} |8 + 7 + 6|$Area $= \frac{1}{2} |21| = 10.5$ square units.

Find the area of the triangle whose vertices are $(2, 3), (-1, 0),$ and $(2, -4)$.

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