Let $A(1, 1)$ be a point. $B$ is the image of $A$ with respect to the line $x + 2y + 2 = 0$. If $C$ is the foot of the perpendicular from $B$ on the line $3x + 4y - 10 = 0$,then $AC$ is equal to

The image of the point $P(3, 8)$ with respect to the line $x + 3y = 7$,assuming the line to be a plane mirror,is equal to .........

The equation of the straight line passing through the point of intersection of the lines $5x - 6y - 1 = 0$ and $3x + 2y + 5 = 0$ and perpendicular to the line $3x - 5y + 11 = 0$ is

The image of a point $(2, -1)$ with respect to the line $x - y + 1 = 0$ 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 $c$.

The orthocentre and the centroid of $\triangle ABC$ are $(5,8)$ and $\left(3, \frac{14}{3}\right)$ respectively. The equation of the side $BC$ is $x-y=0$. Given that the image of the orthocentre of a triangle with respect to any side lies on the circumcircle of that triangle,then the diameter of the circumcircle of $\triangle ABC$ is