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

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)

Answer 2

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