Question

Nathan 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 C to point D?

Answer 1

The formula determine the distance from C to D is:

`√((0-a)^2+(-b)^2)=√(a^2)=a`

Explanation:

The formula that can be used to determine the distance from point C to point D is:

`√((0-a)^2+(-b)^2)=√(a^2)=a`

We know that distance between two points A(a,b) and B(c,d) is equal to the length of the line segment AB and is calculated by the help of the formula:

`√((c-a)^2+(b-d)^2)`

So, here we have:

(a,b)=(a,b) and (c,d)=(0,b)