Nathan wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. He places parallelogram A
BCD 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?
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.
So you want to start to factor so you get (x²+2)(x²-7) = 0. Now set each () to 0, so you get (x²+2) = 0 and (x²-7)=0. The first ends with +√2i and -√2i, the second ends with +√7 and -√7