How to find area of rectangle on coordinate graph?

Answer 1

Suppose the sides of the rectangle ABCD are not parallel to the axis.

Then if A = (p,q) and B = (r, s)

then by Pythagoras, |AB|2 = (p - r)2 + (q - s)2 from which AB can be calculated.

Calculate BC in a similar fashion and then area = AB*BC

If AB is parallel to an axis (say the x axis), then q = s so that q - s = 0 and

|AB|2 simplifies to (p - r)2 + 02

so that |AB| = |p - r|