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The end points of one side of a regular pentagon are (-1,4) and (2,3). What is the perimeter of the pentagon?

(1) the square root of 10
(2) 5 times the square root of 10
(3) 5 times the square root of 2
(4) 25 times the square root of 2

The end points of one side of a regular pentagon are (-1,4) and (2,3). What is the-example-1
User Max Banaev
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2 Answers

4 votes

the answer is (2) because using the distance formula which can be found on your browser, it will lead us to the answer 5 radical 10

User BoeseB
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7.6k points
5 votes
To determine the perimeter of the pentagon, you must first calculate a side length of it. Let's name the coordinates A(-1,4) and B(2,3).

To figure out how far the points are from each other, you have to use the distance formula:

D_(AB) = \sqrt{( x_(2)-x_(1))^2+{(y_(2)-y_(1))^2}

x_(1) =1, x_(2) =-2, y_(1) =2, y_(2) =3

D_(AB)= \sqrt{(2--1)^2+{(3-4)^2}
D_{AB}= \sqrt{(2--1)^2+{(3-4)^2}

D_(AB)= \sqrt{(2+1)^2+{(3-4)^2}

D_(AB)= √((3)^2+(-1)^2)

D_(AB)= √(9+1)

D_(AB)= √(10)

Now, the formula for the perimeter of a pentagon is
P = 5×side length

So...
Perimeter = 5×
√(10)

The answer is (2)

User Jardine
by
7.7k points

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