The distance between the point $(2, 1)$ and the image of the point $(3, -1)$ with respect to the line $2x + y - 1 = 0$ is

The perpendicular from the origin to the line $y=mx+c$ meets it at the point $(-1, 2)$. Find the values of $m$ and $c$.

If $Q$ is the image of the point $P(1,1)$ with respect to the straight line $x+y+1=0$,then the length of the perpendicular drawn from $Q$ to the line $3x-4y+3=0$ is

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

If the reflection of a point $A(2,3)$ in the $X$-axis is $B$; the reflection of $B$ in the line $x+y=0$ is $C$,and the reflection of $C$ in $x-y=0$ is $D$,then the point of intersection of the lines $CD$ and $AB$ is:

Let $P$ be an interior point of a $\triangle ABC$. Let $Q$ and $R$ be the reflections of $P$ in $AB$ and $AC$,respectively. If $Q, A, R$ are collinear,then $\angle A$ equals (in $^{\circ}$)