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

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

Answer 2

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) }`