The diagonals of a parallelogram $PQRS$ are along the lines $x + 3y = 4$ and $6x - 2y = 7$. Then $PQRS$ must be a

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?

What is the ratio of the area of $\triangle PQS$ to the area of $\triangle PQR$?

The four points whose coordinates are $(2, 1), (1, 4), (4, 5), (5, 2)$ form:

The coordinates of the feet of the perpendiculars from the vertices of a triangle to the opposite sides are $(20, 25)$,$(8, 16)$,and $(8, 9)$. Find the orthocenter of the triangle.

Let $PQR$ be a triangle in which $PQ=3$. From the vertex $R$,draw the altitude $RS$ to meet $PQ$ at $S$. Assume that $RS=\sqrt{3}$ and $PS=QR$. Then,$PR$ equals