### Lines and Triangles

goals
Two equal sides of an isosceles triangle are given by the equations $7x - y + 3 = 0$ and $x + y - 3 = 0$ and its third side passes through the point $(1, -10)$. Determine the equation of the third side.
Find foot of the $\perp$ from the point (2, 3) on the line $3x-y+4=0$
Let $A(3,\ 2,\ 0),\ B(5,\ 3,\ 2),\ C(-9,\ 6,\ -3)$ be three points forming a triangle. $AD$, the bisectors of $\angle BAC$,meets $BC$ an $D$. Find the coordinates of the point $D$.
$PQRS$ is a square, $T$ and $U$ are the mid-points of the sides $PS$ and $QR$ respectively. find the area of  $\Delta OTS$, if $PS=8cm$,where O is the point of intersection of $TU$ and $OS$.
In a $\triangle ABC$ right angled at C, if $\tan { A=\frac { 1 }{ \sqrt { 3 } } }$ find the value of $\sin { A } \cos { B } +\cos { A } \sin { B }$