Question

What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?

15.3 units

20.4 units

30.6 units

52.0 units

Answer 1

The perimeter of the rectangle shown on the coordinate plane of points (-6,4), (-7,-1), (3,-3) and (4,2) is 30.6 units. The length of one side of the rectangle is 5.10 units and the other side is 10.20 units. To calculate the perimeter of a rectangle 2L+2W= 30.6 units.

Answer 2

see the attached figure to better understand the problem

Let

x------> the length side of a rectangle

y-------> the width side of a rectangle

we know that

the perimeter of a rectangle is equal to the formula

`P=2x+2y`

In this problem

`AB=DC=x\\AD=BC=y`

Step 1

Find the distance AB

`A(-6,4)\\B(4,2)`

we know that

the distance's formula between two points is equal to

`d=\sqrt{(y2-y1)^(2) +(x2-x1)^(2)}`

substitute the values

`dAB=\sqrt{(2-4)^(2) +(4+6)^(2)}`

`dAB=\sqrt{(-2)^(2) +(10)^(2)}`

`dAB=√(104)\ units=10.2\ units`

Step 2

Find the distance BC

`B(4,2)\\C(3,-3)`

we know that

the distance's formula between two points is equal to

`d=\sqrt{(y2-y1)^(2) +(x2-x1)^(2)}`

substitute the values

`dBC=\sqrt{(-3-2)^(2) +(3-4)^(2)}`

`dBC=\sqrt{(-5)^(2) +(-1)^(2)}`

`dBC=√(26)\ units=5.1\ units`

Step 3

Find the perimeter

we know that

the perimeter of a rectangle is equal to the formula

`P=2x+2y`

`P=2AB+2BC`

substitute the values of the distance in the formula

`P=2*10.2+2*5.1=30.6\ units`

therefore

the answer is

The perimeter of the rectangle is equal to
`30.6\ units`