To find the perimeter of the triangle formed by the points (-1, 2), (0, 2), and (-1, -2), we first need to calculate the lengths of the three sides of the triangle using the distance formula:
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Step 1: Calculate the lengths of the sides
Side 1: Between points (-1, 2) and (0, 2)
\[ d_1 = \sqrt{(0 - (-1))^2 + (2 - 2)^2} = \sqrt{(1)^2 + (0)^2} = \sqrt{1} = 1 \]
Side 2: Between points (0, 2) and (-1, -2)
\[ d_2 = \sqrt{((-1) - 0)^2 + (-2 - 2)^2} = \sqrt{(-1)^2 + (-4)^2} = \sqrt{1 + 16} = \sqrt{17} \]
Side 3: Between points (-1, -2) and (-1, 2)
\[ d_3 = \sqrt{((-1) - (-1))^2 + (2 - (-2))^2} = \sqrt{(0)^2 + (4)^2} = \sqrt{16} = 4 \]
Step 2: Calculate the perimeter
Now, we can add the lengths of the sides to find the perimeter:
\[ \text{Perimeter} = d_1 + d_2 + d_3 = 1 + \sqrt{17} + 4 \]
Now we calculate \(\sqrt{17}\):
\[ \sqrt{17} \approx 4.123 \]
So the perimeter becomes:
\[ \text{Perimeter} \approx 1 + 4.123 + 4 = 9.123 \]
Step 3: Round to the nearest tenth
Rounding 9.123 to the nearest tenth gives:
\[ \text{Perimeter} \approx 9.1 \]
Thus, the perimeter of the triangle is approximately 9.1 units.