He coordinates of the vertices of a polygon are (−2,−2), (3,−3), (4,−6), (1,−6), and (−2,−4). what is the perimeter of the polygon to the nearest tenth of a unit?

  16.9

Step-by-step explanation:

The distance formula can be used to find the lengths of individual segments. It tells you ...

 d = √((Δx)² +(Δy)²)

where Δx and Δy are the differences between x- and y-coordinates of the segment end points.

Since the value is squared, the sign of the difference doesn't matter. It can be easier to write it as always positive, so in some cases it may be Δx = x₂-x₁ and in other cases it might be Δx = x₁-x₂, for example.

If the segments are labeled A, B, C, D, E in order, the distances are ...

 AB = √(5²+1²) = √26 ≈ 5.099

 BC = √(1²+3²) = √10 ≈ 3.162

 CD = Δx = 3

 DE = √(3²+2²) = √13 ≈ 3.606

 EA = Δy = 2

Then the perimeter is ...

 P = AB +BC +CD +DE +EA = 5.099 +3.162 +3 +3.606 +2 = 16.867

 P ≈ 16.9