The equation of a line passing through $(1, -2)$ and perpendicular to the line $3x - 5y + 7 = 0$ is

Let $ABC$ be a triangle and $A=(1,2)$. If $x-3y-5=0$ and $x+5y-9=0$ are the perpendicular bisectors of the sides $AB$ and $BC$ respectively,then the length of the side $AC$ is

The image of the point $(6, 5)$ in the line $x = 3$ is

If $PM$ is the perpendicular from $P(2, 3)$ onto the line $x + y = 3$,then the coordinates of $M$ are

Let $P$ be a point inside a $\triangle ABC$ with $\angle ABC = 90^{\circ}$. Let $P_1$ and $P_2$ be the images of $P$ under reflection in $AB$ and $BC$ respectively. The distance between the circumcenters of $\triangle ABC$ and $\triangle P_1PP_2$ is

In a triangle $ABC$,$A(3, 5)$ is a vertex. If the internal angle bisector of $B$ is $y = x$,then which of the following points must lie on the line $BC$?