The opposite vertices of a square are $(1, 2)$ and $(3, 8)$. Then,the equation of the diagonal of the square passing through the point $(1, 2)$ is:

$A$ ray of light coming from the point $(2, 2\sqrt{3})$ is incident at an angle $30^{\circ}$ with the normal to the line $x=1$ at the point $A$. The ray gets reflected on the line $x=1$ and meets the $x$-axis at the point $B$. Then,the line $AB$ passes through the point

The equation of the straight line whose slope is $\frac{-2}{3}$ and which divides the line segment joining $(1, 2)$ and $(-3, 5)$ in the ratio $4:3$ externally is

$A$ line passing through the point $A(2, 3)$ makes an angle of $45^{\circ}$ with the $x$-axis and intersects the line $x + y + 1 = 0$ at point $P$. Find the distance $AP$.

The polar equation of the line perpendicular to the line $\sin \theta - \cos \theta = \frac{1}{r}$ and passing through the point $\left(2, \frac{\pi}{6}\right)$ is

Reduce the following equation into intercept form and find its intercepts on the axes: $3x + 2y - 12 = 0$.