Question

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

Answer 1

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

Answer 2

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)