Question

Please help me, The vertices of quadrilateral COAT are C(2,0), O(7,0), A(7,2) and T(2,2). Prove that COAT is a rectangle.

Answer 1

thank you

Explanation:

so so so much ^^^

Answer 2

ANSWER

Opposite sides of COAT are parallel and adjacent sides are perpendicular.

EXPLANATION

It is sufficient to prove that, the opposite sides of COAT are parallel and the adjacent sides are perpendicular.

C(2,0) and O(7,0) form side CO of the rectangle.

The slope of this side is


`= (0 - 0)/(7 - 2) = 0`
O(7,0), A(7,2) form side OA of the rectangle.

The slope is


`= (2 - 0)/(7 - 7) = (2)/(0)`

This is an undefined slope. This means that side OA of the rectangle is a vertical line and perpendicular to side CO.

A(7,2) and T(2,2) formed side AT of the rectangle.

This side has slope


`= (2 - 2)/(7 - 2) = (0)/(5) = 0`

This side is also parallel to CO and perpendicular to AT.

Finally T(2,2),C(2,0) formed side TC of the rectangle.

The slope is

`= (2 - 0)/(2 - 2) = (2)/(0)`

This slope is also undefined. This means that OA is parallel to TC and perpendicular to AT and CO.

Hence COAT is a rectangle.