In each of the following,find the value of k | vedclass

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(B) For points to be collinear,the area of the triangle formed by them must be equal to $0$.The formula for the area of a triangle with vertices $(x_1

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$4$

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(B) For points to be collinear,the area of the triangle formed by them must be equal to $0$.The formula for the area of a triangle with vertices $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ is $\frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = 0$.Substituting the given points $(7, -2), (5, 1),$ and $(3, k)$ into the formula:$\frac{1}{2} |7(1 - k) + 5(k - (-2)) + 3(-2 - 1)| = 0$$\frac{1}{2} |7 - 7k + 5(k + 2) + 3(-3)| = 0$$\frac{1}{2} |7 - 7k + 5k + 10 - 9| = 0$$|8 - 2k| = 0$$8 - 2k = 0$$2k = 8$$k = 4$

In each of the following,find the value of $k$ for which the points are collinear: $(7, -2), (5, 1), (3, k)$.

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