A. Derive the distance formula (d) shown below for points A = (x1, y1) and B = (x2, y2).

Question

2
2 1
2
2 1 d = (x − x ) + ( y − y )
Note: Look for an application of the Pythagorean theorem where the red line, segment
AB, is the hypotenuse of a right triangle. You can then determine the lengths of the legs
and justify why they meet at right angles.

Answer 1

d = sqrt [ ( x2 - x1 ) ^ 2 + ( y2 - y1 ) ^ 2 ]