2000 AMC 10 Question 5

Points $M$ and $N$ are the midpoints of sides $PA$ and $PB$ of $\triangle PAB.$ As $P$ moves along a line that is parallel to side $AB,$ how many of the four quantities listed below change?

(a) the length of the segment $MN;$ (b) the perimeter of $\triangle PAB;$ (c) the area of $\triangle PAB;$ (d) the area of trapezoid $ABNM.$