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 $BC$?

The length of the perpendicular from the origin,on the normal to the curve $x^{2}+2xy-3y^{2}=0$ at the point $(2,2)$ is

$A$ ray of light passing through the point $(2, 3)$ reflects on the $Y$-axis at a point $P$. If the reflected ray passes through the point $(3, 2)$ and $P = (a, b)$,then $5b =$

The coordinates of the foot of the perpendicular from $(0,0)$ upon the line $x+y=2$ are

The equation of the line bisecting the line segment joining the points $(a, b)$ and $(a', b')$ at a right angle is

Let $Q$ be the image of a point $P(1, 2)$ with respect to the line $x + y + 1 = 0$ and $R$ be the image of $Q$ with respect to the line $x - y - 1 = 0$. If $M$ and $N$ are the midpoints of $PQ$ and $QR$ respectively,then $MN =$