Question

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.

Answer 1

To prove that quadrilateral COAT is a rectangle, we can use the slope formula to show that opposite sides of the quadrilateral are parallel and equal in length.

Step-by-step explanation:

To prove that quadrilateral COAT is a rectangle, we can use the slope formula to show that opposite sides of the quadrilateral are parallel and equal in length.

First, we calculate the slopes of the lines CO and AT using the formula m = (y2 - y1)/(x2 - x1).

mCO = (0 - 0)/(5 - 0) = 0 and mAT = (2 - 2)/(0 - 5) = 0.

Since the slopes of both CO and AT are 0, we can conclude that these two sides are horizontal and parallel. By the same reasoning, we can show that sides OA and CT are vertical and parallel, resulting in a rectangle.

Answer 2

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).