SOLUTION: is this quadrilateral, with the given vertices, a rectangle, by using coordinate geometry? A(4,1), B(0,7), C(3,9), D(7,3)

First let's draw it on graph paper to see what we think it is:



It looks like a rectangle. To prove that it is a rectangle by coordinate
geometry, show that it is a parallelogram with one right interior angle:

1. Use the slope formula to find the slopes of all four sides.
2. Show that both pairs of opposite sides have the same slope.

That's enough to show that it is a parallelogram.
Then, to show that it is has one right angle, show that any one pair
of adjacent sides have slopes which are negative reciprocals of each other.

(If a parallelogram has one right angle, then the other three are
automatically right angles, too.)

Edwin