Question

PLEASE HELP!! (50 POINTS)

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.
-I need the Parallelogram Method (Slope Formula) & Rectangle Method (Distance or Slope Formula).

Answer 1

Since pair of opposite sides are parallel and adjacent sides meets at right angles, the quadrilateral COAT is a rectangle.

Explanation:

The vertices of the given quadrilateral is
`C(2,0),O(7,0),A(7,2),T(2,2)`

It is sufficient to show that pair of opposite sides are parallel and adjacent sides are perpendicular.

The slope of each side can be found using the formula;

`m=(y_2-y_1)/(x_2-x_1)`

Slope of CO,

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

A line with a zero slope is a horizontal line.

The slope of OA,

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

This slope is undefined.

A line with an undefined slope is a vertical line.

This shows that,the side CO and OA of the quadrilateral meets at right angle.

The slope of AT,

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

This is also a horizontal line.

The slope of TC,

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

This also a vertical line.

This implies that, side TC and side AT meets at Tat right angles and TC is parallel to OA.

Also AT is parallel to TO.

This shows that COAT is a rectangle.