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)
