Find the equation of the line joining (3, 1) | vedclass

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(B) Let $P(x, y)$ be any point on the line joining the points $A(3, 1)$ and $B(9, 3)$.Since the points $A, B,$ and $P$ are collinear,the area of the t

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$x - 3y = 0$

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(B) Let $P(x, y)$ be any point on the line joining the points $A(3, 1)$ and $B(9, 3)$.Since the points $A, B,$ and $P$ are collinear,the area of the triangle formed by these three points must be zero.The area of the triangle is given by the determinant formula:$\frac{1}{2} \begin{vmatrix} 3 & 1 & 1 \ 9 & 3 & 1 \ x & y & 1 \end{vmatrix} = 0$Expanding the determinant along the first row:$\frac{1}{2} [3(3 - y) - 1(9 - x) + 1(9y - 3x)] = 0$$3(3 - y) - (9 - x) + (9y - 3x) = 0$$9 - 3y - 9 + x + 9y - 3x = 0$Combining like terms:$(x - 3x) + (9y - 3y) + (9 - 9) = 0$$-2x + 6y = 0$Dividing by $-2$:$x - 3y = 0$Thus,the equation of the line is $x - 3y = 0$.

Find the equation of the line joining $(3, 1)$ and $(9, 3)$ using determinants.

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