If $(0, 0), (1, 2),$ and $(-3, 4)$ are the midpoints of the sides of a triangle $ABC$,find the area of triangle $ABC$.

The area (in square units) of the triangle formed by the points with polar coordinates $(1, 0)$,$(2, \frac{\pi}{3})$,and $(3, \frac{2\pi}{3})$ is:

Find the area of a triangle given that midpoints of its sides are $(2, 7)$,$(1, 1)$,and $(10, 8)$.

$A$ triangular corner is cut from a rectangular piece of paper and the resulting pentagon has sides $5, 6, 8, 9, 12$ in some order. The ratio of the area of the pentagon to the area of the rectangle is

$OPQR$ is a square and point $Q$ is $(\alpha, \alpha)$. If $M$ and $N$ are the midpoints of sides $PQ$ and $QR$ respectively,then what is the ratio of the area of the square to the area of triangle $OMN$?

The midpoints of the three sides of a triangle are $(1, 2)$,$(-1, 1)$,and $(0, 3)$. The area of this triangle is (in sq. units):