The foot of the perpendicular from the point $(2,4)$ upon the line $x+y=4$ is:

If the point $P(4,1)$ undergoes a reflection in the line $x-y=0$,then a translation through a distance of $2$ units along the positive $X$-axis and finally projected on the $X$-axis,then the coordinates of $P$ in the final position are

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

$A$ person standing at the junction of two straight paths represented by the equations $2x - 3y + 4 = 0$ and $3x + 4y - 5 = 0$ wants to reach the path whose equation is $6x - 7y + 8 = 0$ in the least time. Find the equation of the path that he should follow.

The image of the point $(4, -13)$ with respect to the line $5x + y + 6 = 0$ is

If the image of $\left(\frac{-7}{5}, \frac{-6}{5}\right)$ in a line is $(1, 2)$,then the equation of the line is