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 x_{1} (y_{2}-y_{3}) + x_{2 }(y_{3}-y_{1}) + x_{3 }(y_{1}-y_{2})

= 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