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Q.
$A B C$ is an isosceles triangle. If the coordinates of the base are $B(1,3)$ and $C(-2,7)$, the coordinates of vertex $A$ can be
Straight Lines
Solution:
Let the vertex of triangle be $A(x, y)$. Then the vertex $A(x, y)$ is equidistant from $B$ and $C$ because $A B C$ is an isosceles triangle. Therefore,
$(x-1)^{2}+(y-3)^{2}=(x+2)^{2}+(y-7)^{2}$
or $6 x-8 y+43=0$
Thus, any point lying on this line can be the vertex $A$ except the midpoint $(-1 / 2,5)$ of $B C$.
Hence, vertex $A$ is $(5 / 6,6)$.