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(B) 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

$3$

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(B) 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 $A(5, 3)$,$B(4, 5)$,and $C(3, 1)$.Here,$x_1 = 5, y_1 = 3, x_2 = 4, y_2 = 5, x_3 = 3, y_3 = 1$.Substituting these values into the formula:Area $= \frac{1}{2} |5(5 - 1) + 4(1 - 3) + 3(3 - 5)|$Area $= \frac{1}{2} |5(4) + 4(-2) + 3(-2)|$Area $= \frac{1}{2} |20 - 8 - 6|$Area $= \frac{1}{2} |6| = 3 	ext{ square units}$.Thus,the correct option is $B$.

Find the area of a triangle having the vertices $A(5, 3)$,$B(4, 5)$,and $C(3, 1)$.

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