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zavuch27 [327]
3 years ago
9

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

Mathematics
1 answer:
marissa [1.9K]3 years ago
8 0
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}= \sqrt{(3)^2+(-1)^2}
D_{AB}= \sqrt{9+1}
D_{AB}= \sqrt{10}

Now, the formula for the perimeter of a pentagon is 
P = 5×side length
 
So...
Perimeter = 5×\sqrt{10}

The answer is (2)

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