On your paper, construct a rectangle on a coordinate plane that satisfies these criteria. • The sides of the rectangle are either vertical or horizontal.

• The perimeter of the rectangle is 42 units.

• Each of the vertices lies in a different quadrant.

What are the coordinates of the vertices of your rectangle? Explain how you know the perimeter of your rectangle is

42 units

Step-by-step explanation:

Required

Construct a rectangle whose perimeter is 42 units and satisfies the given conditions.

First, name the rectangle ABCD.

Such that:

For the rectangle to be either horizontal or vertical, then:

and

We have that:

Replace perimeter with its formula

Divide both sides by 2

This implies that, the distance between adjacent sides (through the edges) must be equal to 21

Having said that: a set of coordinates that satisfy the given conditions are:

-- First quadrant

-- Second quadrant

-- Third quadrant

-- Fourth quadrant

The above quadrants satisfy the condition:

and

HOW TO KNOW THE PERIMETER IS 42

To do this, we simply calculate the distance between the edges and add them up

Distance is calculated as:

For AB

For BC

For CD

For DA

So, the perimeter is:

See attachment for rectangle

step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15