If the three points A(1, 6),B(3, -4),and C(x, | vedclass

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(A) For three points $A(x_1, y_1)$,$B(x_2, y_2)$,and $C(x_3, y_3)$ to be collinear,the area of the triangle formed by them must be zero,or the slope o

Vedclass · Accepted Answer

$5x + y - 11 = 0$

Vedclass · Answer

(A) For three points $A(x_1, y_1)$,$B(x_2, y_2)$,and $C(x_3, y_3)$ to be collinear,the area of the triangle formed by them must be zero,or the slope of $AB$ must equal the slope of $BC$. Using the determinant method: $\begin{vmatrix} 1 & 6 & 1 \ 3 & -4 & 1 \ x & y & 1 \end{vmatrix} = 0$ Expanding along the first row: $1(-4 - y) - 6(3 - x) + 1(3y - (-4x)) = 0$ $-4 - y - 18 + 6x + 3y + 4x = 0$ $10x + 2y - 22 = 0$ Dividing by $2$: $5x + y - 11 = 0$

If the three points $A(1, 6)$,$B(3, -4)$,and $C(x, y)$ are collinear,then the equation satisfied by $x$ and $y$ is:

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