Find the perimeter of the polygon defined by the coordinates (5, 12), (12, 0), (0, 0), and (-4, 12). (Round to nearest tenth) A) 42.5 units B) 47.5 units C) 52.5 units D) 57.5 units

To find the perimeter of the polygon, we need to calculate the lengths of its sides using the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[ \text{distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Let's label the points: A = (5, 12) B = (12, 0) C = (0, 0) D = (-4, 12)

Now, we find the distances between consecutive points (sides of the polygon):

AB: \[ \text{distance} = \sqrt{(12 - 5)^2 + (0 - 12)^2} = \sqrt{7^2 + (-12)^2} = \sqrt{49 + 144} = \sqrt{193} \] BC: \[ \text{distance} = \sqrt{(0 - 12)^2 + (0 - 0)^2} = \sqrt{(-12)^2} = \sqrt{144} = 12 \] CD: \[ \text{distance} = \sqrt{(-4 - 0)^2 + (12 - 0)^2} = \sqrt{(-4)^2 + 12^2} = \sqrt{16 + 144} = \sqrt{160} \] DA: \[ \text{distance} = \sqrt{(5 - (-4))^2 + (12 - 12)^2} = \sqrt{9^2} = \sqrt{81} = 9 \]

Now, add these distances together to get the perimeter of the polygon: \[ P = AB + BC + CD + DA \] \[ P = \sqrt{193} + 12 + \sqrt{160} + 9 \]

We can calculate these using a calculator: \[ P \approx 13.9 + 12 + 12.6 + 9 \] \[ P \approx 47.5 \]

Therefore, the perimeter of the polygon is approximately 47.5 units. The correct answer is B) 47.5 units.