Question

Parallelogram ABCD has vertices: A(-3, 1), B(3, 3), C(4, 0), and D(-2, -2). In two or more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rectangle.

Answer 1

Explanation:

If it is a rectangle all the angles between the sides will be 90 degrees. In other words all lines are perpendicular to their joining line.

To find if that is true we can work out the slope of one line (m) and if the line joining it has slope -1/m then they are perpendicular.

So Find the Slope of line segment AB:

m = (3 - 1)/ (3 - -3) = 2/6 = 1/3.

Now BC:

m = (0 - 3)/(4-1) = -3.

If m = 1/3 the -1/m = -1 / 1/3 = -3

- therefor BC is perpendicular to AB.

We can apply the same test to the other pairs of points so as to prove this is a rectangle.