What is the perimeter of this polygon? Round your answer to the nearest tenth. The vertices are (2,3), (-4, 0), and (0, -4). A. 24.0 units B. 21.6 units C. 24.6 Units D. 23.3 units

To find the perimeter of a polygon with given vertices, you need to find the lengths of all its sides and sum them up. The polygon described in your question is a triangle. The vertices are (2,3), (-4, 0), and (0, -4). We can use the distance formula to find the length of each side.

The distance formula is \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of two points.

First, let's find the length of the side between vertices (2,3) and (-4,0). Distance = \(\sqrt{((-4) - 2)^2 + (0 - 3)^2}\) = \(\sqrt{(-6)^2 + (-3)^2}\) = \(\sqrt{36 + 9}\) = \(\sqrt{45}\) = 6.7 units (rounded to the nearest tenth)

Next, find the length of the side between vertices (-4,0) and (0,-4). Distance = \(\sqrt{(0 - (-4))^2 + ((-4) - 0)^2}\) = \(\sqrt{4^2 + (-4)^2}\) = \(\sqrt{16 + 16}\) = \(\sqrt{32}\) = 5.7 units (rounded to the nearest tenth)

Finally, find the length of the side between vertices (0,-4) and (2,3). Distance = \(\sqrt{(2 - 0)^2 + (3 - (-4))^2}\) = \(\sqrt{2^2 + 7^2}\) = \(\sqrt{4 + 49}\) = \(\sqrt{53}\) = 7.3 units (rounded to the nearest tenth)

The perimeter is the sum of all side lengths: Perimeter = 6.7 + 5.7 + 7.3 = 19.7 units (rounded to the nearest tenth)

So the perimeter is closest to 19.7 units, but this is not one of the answer choices you provided.

Given the options, there might be a mistake in either the calculation or the provided answer choices. Please verify the details once again to ensure accuracy.