The area of a triangle is 13 sq. units whose | vedclass

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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

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$2$

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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 $A(8, 2)$,$B(k, 4)$,and $C(6, 7)$ and Area $= 13$. Substituting the values: $13 = \frac{1}{2} |8(4 - 7) + k(7 - 2) + 6(2 - 4)|$ $26 = |8(-3) + 5k + 6(-2)|$ $26 = |-24 + 5k - 12|$ $26 = |5k - 36|$ This gives two cases: Case $1$: $5k - 36 = 26 \implies 5k = 62 \implies k = 12.4$ Case $2$: $5k - 36 = -26 \implies 5k = 10 \implies k = 2$ Since $k$ must be an integer,the value is $k = 2$.

The area of a triangle is $13$ sq. units whose vertices are $A(8, 2)$,$B(k, 4)$,and $C(6, 7)$. Then,the integer value of $k$ is . . . . . . .

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