Question

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

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

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

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

$dAB=\sqrt{104}\ units=10.2\ units$

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

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

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

$dBC=\sqrt{26}\ units=5.1\ units$

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 $30.6\ units$