In an isosceles $\triangle A B C$, the coordinates of vertices $B$ and $C$ of the base $B C$ are $(3,2)$ and…

In an isosceles $\triangle A B C$, the coordinates of vertices $B$ and $C$ of the base $B C$ are $(3,2)$ and $(2,3)$ respectively. If the equation of the line $A B$ is $3 y=2 x$, then the equation of the line $A C$ is
  1. $2 y=3 x$
  2. $2 y=x$
  3. $x+y=0$
  4. $2 x-y=0$

Solution

$\triangle A B C$ is an isosceles triangle $B \equiv(3,2)$ and $C \equiv(2,3)$
$B$ and $C$ are symmetric about the line $y=x$ Equation of $A B=3 y=2 x$ Equation of $A C$ is symmetric about $y=x$ $\therefore$ Equation of $A C=2 y=3 x$

Asked in: AP EAMCET 2021 (25 Aug Shift 1)

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