To calculate the perimeter of the triangle formed by the given coordinates, we first need to determine the exact coordinates from the information you provided. It seems the coordinates for points A, B, and C are partially obscured or jumbled.
Assuming standard coordinates based on your provided values, let’s consider the following points based on the common placement of x and y coordinates:
- Point A = (x1, y1)
- Point B = (x2, y2)
- Point C = (x3, y3)
Let’s assign the coordinates explicitly based on my interpretation of your provided numbers:
- Point A = (-3, 3)
- Point B = (-1, 2)
- Point C = (1, -1)
Next, we will calculate the lengths of the sides of the triangle using the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
1. Length of side AB:
\[ AB = \sqrt{((-1) - (-3))^2 + (2 - 3)^2} = \sqrt{(2)^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.24 \]
2. Length of side BC:
\[ BC = \sqrt{(1 - (-1))^2 + (-1 - 2)^2} = \sqrt{(2)^2 + (-3)^2} = \sqrt{4 + 9} = \sqrt{13} \approx 3.61 \]
3. Length of side CA:
\[ CA = \sqrt{((-3) - 1)^2 + (3 - (-1))^2} = \sqrt{(-4)^2 + (4)^2} = \sqrt{16 + 16} = \sqrt{32} \approx 5.66 \]
4. Calculate the perimeter:
Now, we sum the sides to get the perimeter: \[ \text{Perimeter} = AB + BC + CA \approx 2.24 + 3.61 + 5.66 \approx 11.51 \]
Rounding to the nearest tenth, the perimeter of the triangle is approximately: \[ \text{Perimeter} \approx 11.5 \text{ units} \]
So, the answer is: The perimeter is approximately 11.5 units.