Question

Miguel wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. He places parallelogram ABCD in the coordinate plane so that A is (0, 0), B is (a, 0), C is (a, b), and D is (0, b).

What formula can he use to determine the distance from point A to point B?

Answer 1

By graphing the given points, you will see that a rectangle can be made from the points. Points A and B lie on the same line horizontally as well as points C and D. To determine the distance between points, we use the distance formula expressed as:

d = √((y2-y1)^2 + (x2-x1)^2)

For points A and B, the term (y2-y1)^2 is equal to zero since they lie on the x-axis. The formula would become

d = √(x2-x1)^2
d = x2-x1 = a - 0 = a

Therefore, the distance would be equal to the value of a.