In an isosceles triangle ABC,the coordinates | vedclass

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(A) Given that $	riangle ABC$ is an isosceles triangle with base $BC$ where $B \equiv (3, 2)$ and $C \equiv (2, 3)$.Note that the points $B(3, 2)$ an

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$2y = 3x$

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(A) Given that $	riangle ABC$ is an isosceles triangle with base $BC$ where $B \equiv (3, 2)$ and $C \equiv (2, 3)$.Note that the points $B(3, 2)$ and $C(2, 3)$ are symmetric with respect to the line $y = x$.Since the triangle is isosceles with base $BC$,the vertex $A$ must lie on the perpendicular bisector of $BC$. The perpendicular bisector of the segment joining $(3, 2)$ and $(2, 3)$ is the line $y = x$.Because the entire configuration is symmetric about the line $y = x$,the line $AC$ is the reflection of the line $AB$ about the line $y = x$.To find the reflection of the line $3y = 2x$ about $y = x$,we swap $x$ and $y$ in the equation.Replacing $x$ with $y$ and $y$ with $x$,we get $3x = 2y$,which is $2y = 3x$.Thus,the equation of the line $AC$ is $2y = 3x$.

In an isosceles $\triangle ABC$,the coordinates of vertices $B$ and $C$ of the base $BC$ are $(3, 2)$ and $(2, 3)$ respectively. If the equation of the line $AB$ is $3y = 2x$,then the equation of the line $AC$ is

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