Find the value of m if the points (5,1), (-2, | vedclass

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Question

(A) Let the points be $A(5, 1)$,$B(-2, -3)$,and $C(8, 2m)$.Since the points are collinear,the area of the triangle formed by them must be $0$.The form

Vedclass · Accepted Answer

$\frac{19}{14}$

Vedclass · Answer

(A) Let the points be $A(5, 1)$,$B(-2, -3)$,and $C(8, 2m)$.Since the points are collinear,the area of the triangle formed by them must be $0$.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 coordinates:$\frac{1}{2} |5(-3 - 2m) + (-2)(2m - 1) + 8(1 - (-3))| = 0$$5(-3 - 2m) - 2(2m - 1) + 8(4) = 0$$-15 - 10m - 4m + 2 + 32 = 0$$-14m + 19 = 0$$14m = 19$$m = \frac{19}{14}$

Find the value of $m$ if the points $(5,1), (-2,-3)$ and $(8,2m)$ are collinear.

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