The equation of a line passing through $(1, -2)$ and perpendicular to the line $3x - 5y + 7 = 0$ is

The point $(2,3)$ is first reflected in the straight line $y=x$ and then translated through a distance of $2$ units along the positive direction of the $X$-axis. The coordinates of the transformed point are

The equation of the line perpendicular to the line $ax + by + c = 0$ and passing through $(a, b)$ is:

Let $ABC$ be a triangle and $A=(1,2)$. If $x-3y-5=0$ and $x+5y-9=0$ are the perpendicular bisectors of the sides $AB$ and $BC$ respectively,then the length of the side $AC$ is

The point $(a, b)$ is the foot of the perpendicular drawn from the point $(3, 1)$ to the line $x + 3y + 4 = 0$. If $(p, q)$ is the image of $(a, b)$ with respect to the line $3x - 4y + 11 = 0$,then $\frac{p}{a} + \frac{q}{b} =$

The image of the point $(4, -3)$ with respect to the line $y = x$ is