The distance between the points `A(-8/5,2)and B(2/5,2)` is:

Options

A. 5 units
B. `-5 units`
C. 2 units
D. 7 units

Answer

To find the distance between the points A(-8/5, 2) and B(2/5, 2), we will use the distance formula. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

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

### Step 1: Identify the coordinates
Let:
- \( A(x_1, y_1) = \left(-\frac{8}{5}, 2\right) \)
- \( B(x_2, y_2) = \left(\frac{2}{5}, 2\right) \)

### Step 2: Substitute the coordinates into the distance formula
Substituting the values into the formula:

\[ d = \sqrt{\left(\frac{2}{5} - \left(-\frac{8}{5}\right)\right)^2 + (2 - 2)^2} \]

### Step 3: Simplify the expression
Calculating the x-coordinates:

\[ \frac{2}{5} - \left(-\frac{8}{5}\right) = \frac{2}{5} + \frac{8}{5} = \frac{10}{5} = 2 \]

Now substituting back into the distance formula:

\[ d = \sqrt{(2)^2 + (0)^2} \]

### Step 4: Calculate the squares
Calculating the squares:

\[ d = \sqrt{4 + 0} = \sqrt{4} \]

### Step 5: Find the square root
Taking the square root:

\[ d = 2 \]

### Final Answer
The distance between the points A and B is \( 2 \) units.

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