Final answer:
To find the perimeter of the polygon, calculate the length of each side using the distance formula and then sum them up. The perimeter of the polygon is 25 units, rounded to the nearest tenth it is 25.0 units.
Step-by-step explanation:
To find the perimeter of a polygon, you need to add up the lengths of all its sides. In this case, the polygon has vertices at (-1,1), D(3,4), E(6,0), F(2,-3), and G(-4,-4).
Using the distance formula, you can find the length of each side and then sum them up to find the perimeter.
The distance between (-1,1) and D(3,4) is √((3-(-1))^2 + (4-1)^2) = √((4)^2 + (3)^2) = √(16 + 9) = √25 = 5
Similarly, the distances between D(3,4) and E(6,0), E(6,0) and F(2,-3), F(2,-3) and G(-4,-4), and G(-4,-4) and (-1,1) are also 5 units.
Therefore, the perimeter of the polygon is 5 + 5 + 5 + 5 + 5 = 25 units.
Rounding to the nearest tenth, the perimeter of the polygon is 25.0 units, which is closest to option D) 26.3 units.