The perimeter of triangle formed by the points (0 , 0) , (2, 0) and (0, 2) is

Options

A. 4 units
B. 6 units
C. `6sqrt2` units
D. `4+2sqrt2` units

Answer

To find the perimeter of the triangle formed by the points (0, 0), (2, 0), and (0, 2), we will follow these steps:

### Step 1: Identify the vertices of the triangle
The vertices of the triangle are given as:
- A = (0, 0)
- B = (2, 0)
- C = (0, 2)

### Step 2: Calculate the lengths of the sides of the triangle
We will calculate the lengths of the sides AB, AC, and BC using the distance formula.

#### Length of AB:
AB is the distance between points A and B.
Using the distance formula:
\[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates of A (0, 0) and B (2, 0):
\[ AB = \sqrt{(2 - 0)^2 + (0 - 0)^2} = \sqrt{2^2} = \sqrt{4} = 2 \]

#### Length of AC:
AC is the distance between points A and C.
Using the distance formula:
\[ AC = \sqrt{(0 - 0)^2 + (2 - 0)^2} = \sqrt{(0 - 0)^2 + 2^2} = \sqrt{4} = 2 \]

#### Length of BC:
BC is the distance between points B and C.
Using the distance formula:
\[ BC = \sqrt{(0 - 2)^2 + (2 - 0)^2} = \sqrt{(-2)^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \]

### Step 3: Calculate the perimeter of the triangle
The perimeter P of the triangle is the sum of the lengths of its sides:
\[ P = AB + AC + BC \]
Substituting the lengths we calculated:
\[ P = 2 + 2 + 2\sqrt{2} = 4 + 2\sqrt{2} \]

### Final Answer:
The perimeter of the triangle formed by the points (0, 0), (2, 0), and (0, 2) is \( 4 + 2\sqrt{2} \) units.

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