A. Derive the distance formula (d) shown below for points A = (x1, y1) and B = (x2, y2).
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.
Note: As this is an exercise in analytic Euclidean geometry in two-space, you should
ignore the three-dimensional aspects of the illustration and imagine that the bottom of
the box is on the Cartesian plane.
1. State each step of your derivation.
2. Provide written justification for each step of your derivation
in a right triangle, a^2 + b^2 = c^2
Draw your right triangle with hypotenuse AB having horizontal leg a and vertical leg b.
a = x2-x1
b = y2-y1
c^2 = (x2-x1)^2 + (y2-y1)^2