The triangle with vertices at $(-2, 2)$,$(2, -2)$,and $(1, 1)$ is:

The equations of sides $AB$,$BC$,and $CA$ of a $\triangle ABC$ are $2x+y=0$,$x+py=q$,and $x-y=3$ respectively. If $P(2,3)$ is its orthocenter,then the value of $p+q$ equals

Let $ABCD$ be a trapezium with $AD$ parallel to $BC$. Assume there is a point $M$ in the interior of the segment $BC$ such that $AB=AM$ and $DC=DM$. Then,the ratio of the area of the trapezium to the area of $\triangle AMD$ is

If the midpoints of the sides of a triangle are $(0, 1), (1, 1),$ and $(1, 0)$,what is the $x$-coordinate of the incenter of the triangle?

The opposite angular points of a square are $(3, 4)$ and $(1, -1)$. Then the coordinates of the other two points are

In a $\triangle ABC$,medians $AD$ and $BE$ are drawn. If $AD = 4$,$\angle DAB = \frac{\pi}{6}$,and $\angle ABE = \frac{\pi}{3}$,then the area of the $\triangle ABC$ is