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 used to find the length of a line segment is the same formula as the Pythagoras theorem.

We take CD as the hypotenuse of the right-angled triangle and the distance between the x-coordinates and y-coordinates as the length of two short sides.

We can write the formula as
CD = $\sqrt{( x_{1}- x_{0}) ^{2}+ ( y_{1}- y_{0}) ^{2} }$
CD = $\sqrt{(a-0)^{2}+ (b-b)^{2} }$

Answer 2

Wrong on apex is is a-0+(b-b)2=a2=a