Question

Use the coordinates (-2,1) (0,2) (-2,-1) (0,-2) and (0,2) to compute the perimeter of the triangle. Round your answer to the nearest tenth

Answer 1

To calculate the perimeter of the triangle formed by the points (-2,1), (0,2), and (-2,-1), we first need to compute the lengths of each side of the triangle.

Let's denote the points as follows:
- A = (-2, 1)
- B = (0, 2)
- C = (-2, -1)

We can use the distance formula to find the lengths of the sides AB, BC, and CA. The distance formula is:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

### Step 1: Calculate the lengths of the sides

**1. Length of AB:**
\[
AB = \sqrt{(0 - (-2))^2 + (2 - 1)^2} = \sqrt{(2)^2 + (1)^2} = \sqrt{4 + 1} = \sqrt{5}
\]

**2. Length of BC:**
\[
BC = \sqrt{((-2) - 0)^2 + ((-1) - 2)^2} = \sqrt{(-2)^2 + (-3)^2} = \sqrt{4 + 9} = \sqrt{13}
\]

**3. Length of CA:**
\[
CA = \sqrt{((-2) - (-2))^2 + (1 - (-1))^2} = \sqrt{(0)^2 + (2)^2} = \sqrt{0 + 4} = \sqrt{4} = 2
\]

### Step 2: Calculate the perimeter

Now we can sum the lengths of the sides to get the perimeter \( P \):

\[
P = AB + BC + CA = \sqrt{5} + \sqrt{13} + 2
\]

### Step 3: Approximate the values

Using approximate values:
- \( \sqrt{5} \approx 2.236 \)
- \( \sqrt{13} \approx 3.606 \)

Calculating the perimeter:

\[
P \approx 2.236 + 3.606 + 2 = 7.842
\]

### Step 4: Round to the nearest tenth

Rounding 7.842 to the nearest tenth, we get:

\[
\text{Perimeter} \approx 7.8
\]

Thus, the perimeter of the triangle is approximately **7.8** units.