If the points A (1,-2) B (2,3)C (-3,2) D (-4,-3) are the vretices of parallelogram ABCD, then taking AB as the base find the height of the parallelogram
Area of a triangleABC = 1/2 x1 (y2-y3) + x2 (y3-y1) + x3 (y1-y2)
= 1/2 1(3-2) + 2(2+2) + (-3)(-2-3) = 1/2 x 1 + 8 + 15 = 1/2 x 24 = 12
since ABCD is a parallelogram
therefore area of parallelogram ABCD = 2 x area of triangle ABC = 2 x 12 = 24
and AB = root of (2-1)2 + (3+2)2 = root of 1 + 25 = root 26
Now, we know that
Area of a parallelogram = base x height
24 = root 26 + height
or height = 24 - root26