What is the reflection of the point $(1, -2)$ with respect to the $y$-axis?

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

$x-y=0$ and $\frac{x}{2}+\frac{y}{2}=1$ are respectively the perpendicular bisectors of the sides $AB$ and $AC$ of a triangle $ABC$. If the vertex is $A(2, 3)$,then the equation of the side $BC$ is

If $A(2, -1)$ and $B(6, 5)$ are two points,the ratio in which the foot of the perpendicular from $P(4, 1)$ to $AB$ divides $AB$ is:

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

The reflection of the point $(4, -13)$ in the line $5x + y + 6 = 0$ is