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 Ais (0,0), B is (a,0), Cis (a, b), and Dis (0, b).
What formula can he use to determine the distance from point C to point D?

C

Step-by-step explanation:

So, first you should draw this rectangle and lable the points accordingly. We can see that the x value of D is 0. That point goes in the bottom left and the A point goes in the top left. You should really draw this while im explaining so it makes more sense.

Now we need to figure out where C and B are. B has a y value of 0, so that means B is in the top right corner. C is in the bottom right.

We have this rectangle labeled now, that was the hard part. We want the distance from C to D. That's essentially Δx, which is (a-0). That just equals a itself. Its either choice A.) or choice C.)

In choice A.), they use 0 - 0 which makes no sense because Δy has no 0 values. We can see our change in y is (b - b). All I did was subtract the two y coords, just like Δx.

Answer C.) fits this perfectly. And I just realized i over complicated this problem. You didnt really have to label these points ABCD. But oh well, I still got the right answer. The 3rd paragraph and on is the only imprtant info