$A(3, -4)$ is a vertex of $\triangle ABC$ and $3x + 4y - 18 = 0$ is the perpendicular bisector of the side $AB$. If $C = (6, 3)$,then the centroid of the triangle is:

Let the mirror image of point $A(1, 4)$ in the line $y = x$ be point $B$; the mirror image of point $B$ in the line $y = -x$ be $C$; and the mirror image of $C$ in the $x$-axis be $D$. Then,the area of triangle $ABD$ is ............... $sq. \, units$.

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

One vertex of the equilateral triangle with centroid at the origin and one side as $x + y - 2 = 0$ is

If a ray travels along the line $x = 1$ and gets reflected by the line $x + y = 1$,find the equation of the reflected ray.

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