Question

A rectangle in the coordinate plane has vertices at (-1, 6), (-1, 2), (4, 2), and (4, 6). The perimeter of the rectangle is Choose... units. The area of the rectangle is Choose... square units.

Answer 1

perimeter = 18 units

area = 20 square units.

Explanation:

We know that a rectangle is defined by two measures, length L, and width W.

Such that the perimeter is given by:

P = 2*(L + W)

and the area is given by:

A = L*W

Here we know that the vertices of or rectangle are:

(-1, 6)

(-1, 2)

(4, 2)

(4, 6)

Here you can see that we have just two different values of x (-1 and 4) and two different values of y (6 and 2)

So we can define the length L as the difference between the two different values of x:

L = 4 - (-1) = 4 + 1 = 5 units

And the width as the difference between the two different values of y:

W = 6 - 2 = 4 units

A graph of the rectangle can be seen below, to see why I choose to define the length and width in this way.

Now that we know the measures of our rectangle, and using the above formulas for perimeter and area, we get:

P = 2*(W + L) = 2*(5 + 4) = 18 units

A = W*L = 5*4 = 20 square units