The exact perimeter of the quadrilateral ABCD plotted is 5 + √85 + 2√65.
What is the distance between two points ( p,q) and (x,y)?
The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
The perimeter of the quadrilateral ABCD is plotted. These are the points:
A(-5,-2)
B(1,5)
C(5,-2)
D(2,-6)
The distance of AB
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.\\\\D = \sqrt{(1-(-5))^2 + (5-(-2))^2} \: \rm units.\\\\D = \sqrt{85}[/tex]
The distance of BC
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.\\\\D = \sqrt{(5-(1))^2 + (-2-(5))^2} \: \rm units.\\\\D = \sqrt{65}[/tex]
The distance of CD
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.\\\\D = \sqrt{(2-(5))^2 + (-6-(-2))^2} \: \rm units.\\\\D = \sqrt{65}[/tex]
The distance of AD
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.\\\\D = \sqrt{(2-(-5))^2 + (-6-(-2))^2} \: \rm units.\\\\D = 5[/tex]
Therefore, The perimeter of the quadrilateral ABCD is 5 + √85 + 2√65.
Learn more about the distance between two points here:
brainly.com/question/16410393
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