The vertices of quadrilateral coat are c(0,0), o(5,0), a(5,2) and t(0,2). prove that coat is a rectangle. all i need is for someone to solve it using slope formula, and explain why it works. i've tried it myself, but i really want an outside source to see if i got it right, and my reasoning correct.

So to prove this you have to show lines matching the points on both sides are parallel, or just draw the thing, and prove that the opposite lines are parallel. To get the slope of a line between to lines you use the formula (y1-y2)/(x1-x2), with point 1 (x1,y1) and point 2 (x2, y2). Check the slope for the opposite sides, and if these are the same, it is a rectangle. The slope of the line between C and O will then be (0-0)/(5-0), or 0, and the opposite would then be AT, so then (2-2)/(5-0), so 0 as well. We are half way there! Next we have OA, which would be (0-2)/(5-5), which is -2/0. If we get a 0 in the denominator, that means the line is vertical. And OA's match is CT, which is (0-2)/(0-0), which is vertical as well. This means it is a rectangle, as the matching sides all were parallel. (vertical = vertical, and 0 = 0) (btw slope of 0 is horizontal).