Question

Polygon ABCD has vertices A(0, 2), B(0, 8), C(7, 8), and D(7, 2). What is polygon ABCD and its perimeter? (Hint: Draw the polygon on the coordinate plane and find the slopes of each side.)

A. rectangle; P = 26 linear units
B. square; P = 42 units2
C. parallelogram; P = 42 linear units
D. trapezoid; P = 26 linear units,

Answer 1

Option A.

Explanation:

The vertices of Polygon ABCD are A(0, 2), B(0, 8), C(7, 8), and D(7, 2).

Plot all vertices on the coordinate place.

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the slope of the line is

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

First we need find the slope of each sides, using the above formula.

`m_(AB)=(8-2)/(0-0)=\infty`

`m_(BC)=(8-8)/(7-0)=0`

`m_(CD)=(8-2)/(7-7)=\infty`

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

The slope of vertical lines is ∞ and slope of horizontal line is 0. It means sides AB and CD are vertical lines and sides BC and AD are horizontal lines.

Vertical and horizontal lines are perpendicular to each other. It means all interior angles of the polygon are right angles.

From the below figure it is clear that

`AB=6`

`BC=7`

`CD=6`

`AD=7`

Opposite sides are equal and interior angles are right angles, so the polygon is a rectangle.

Perimeter of the polygon is

`Perimeter=AB+BC+CD+AD`

`Perimeter=6+7+6+7=26`

Perimeter of polygon ABCD is 26 linear units.

Therefore, the correct option is A.

Answer 2

Polygon ABCD is just a rectangle, because while it has four sides and four right (90 degree) angles, they are not of equal length. (If ABCD had four sides of equal length and four right angles, it would be a square). To find the perimeter of an object, simply add up the lengths of its sides. ABCD's sides have lengths 6, 6, 7, 7. So the sum of the sides is 26. Therefore, A is the correct answer, because it identifies ABCD correctly as a rectangle and gives the proper perimeter of 26 units.