On a coordinate plane, rectangle W X Y Z is shown. Point W is at (negative 6, 6), point X is at (negative 4, 0), point Y is at (negative 7, negative 1), and point Z is at (negative 9, 5).
In the diagram, ZY = WX = 2 StartRoot 10 EndRoot. What is the perimeter of rectangle WXYZ?

StartRoot 10 EndRoot units
2 StartRoot 10 EndRoot units
6 StartRoot 10 EndRoot units
8 StartRoot 10 EndRoot units

6 StartRoot 10 EndRoot units

Step-by-step explanation:

step 1

Plot the coordinates of rectangle WXYZ to better understand the problem

we have

W(-6,6),X(-4,0),Y(-7,-1),Z(-9,5)

using a graphing tool

see the attached figure

step 2

Find out the perimeter

The perimeter of rectangle is equal to

we have

the formula to calculate the distance between two points is equal to

Find the distance WX

we have

W(-6,6),X(-4,0)

substitute in the formula

Find the distance XY

we have

X(-4,0),Y(-7,-1)

substitute in the formula

step 3

Find the perimeter

we have

substitute

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is