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

The foot of the perpendicular drawn from $(2, 4)$ to the line $x + y = 1$ is

Find the equation of the right bisector of the line segment joining the points $(3, 4)$ and $(-1, 2).$

The coordinates of the foot of the perpendicular from the point $(2, 3)$ on the line $y = 3x + 4$ are given by

The value of $a$ for which the image of the point $(a, a - 1)$ with respect to the line mirror $3x + y = 6a$ is the point $(a^2 + 1, a)$ is:

$y-x=0$ is the equation of a side of a triangle $ABC$. The orthocentre and circumcentre of the triangle $ABC$ are respectively $(5,8)$ and $(2,3)$. The reflection of the orthocentre with respect to any side of the triangle lies on its circumcircle. Then the radius of the circumcircle of the triangle is