Atriangle has the vertices: a(-4,7), b(-3, 5) and c(8, -1).
what is the length of the perimeter of the triangle?

You can find the length of the sides using the a result of the Pythagorean Theorem.  Each side is:

s^2=(x2-x1)^2+(y2-y1)^2  so you have:

s1^2=(-3--4)^2+(5-7)^2

s1^2=1+4

s1=√5

s2^2=(8--3)^2+(-1-5)^2

s2^2=121+36

s2=√157

s3^2=(8--4)^2+(-1-7)^2

s3^2=144+64

s3=√208

The perimeter is:

p=s1+s2+s3

p=√5+√157+√208 units

p≈29.19 units (to nearest hundredth)