The point $Q$ is the image of the point $P(1,5)$ about the line $y=x$ and $R$ is the image of the point $Q$ about the line $y=-x$. The circumcentre of the $\Delta PQR$ is

The image of the line $x+y-2=0$ in the $y$-axis is

Let $L$ be the line $y = 2x$ in two dimensions.
Statement-$1$: The reflection of the point $(0, 1)$ in $L$ is the point $(4/5, 3/5)$.
Statement-$2$: The points $(0, 1)$ and $(4/5, 3/5)$ lie on opposite sides of the line $L$ and are equidistant from it.

If the $y$-intercept of the perpendicular bisector of the line segment joining $P(1, 4)$ and $Q(k, 3)$ is $-4$,then a possible value of $k$ is

If $B$ is the reflection of the point $A(1, 2)$ with respect to the line $y = x$ and $(\alpha, \beta)$ is the reflection of $B$ with respect to $y = 0$,then-

If the coordinates of $A$ and $B$ are $(1, 1)$ and $(5, 7)$,then the equation of the perpendicular bisector of the line segment $AB$ is