The distance between the points `P(-(11)/(3), 5)` and Q `(-(2)/(3), 5)` is

Options

A. 6 units
B. 4 units
C. 3 units
D. 2 units

Answer

To find the distance between the points \( P\left(-\frac{11}{3}, 5\right) \) and \( Q\left(-\frac{2}{3}, 5\right) \), we can use the distance formula for two points in a coordinate plane. 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:
- \( P = (x_1, y_1) = \left(-\frac{11}{3}, 5\right) \)
- \( Q = (x_2, y_2) = \left(-\frac{2}{3}, 5\right) \)

### Step 2: Substitute the coordinates into the distance formula
Now, substitute the coordinates into the distance formula:

\[ D = \sqrt{\left(-\frac{2}{3} - \left(-\frac{11}{3}\right)\right)^2 + (5 - 5)^2} \]

### Step 3: Simplify the expression
First, simplify the expression inside the square root:

1. Calculate \( x_2 - x_1 \):
\[ -\frac{2}{3} - \left(-\frac{11}{3}\right) = -\frac{2}{3} + \frac{11}{3} = \frac{11 - 2}{3} = \frac{9}{3} = 3 \]

2. Calculate \( y_2 - y_1 \):
\[ 5 - 5 = 0 \]

Now substitute these values back into the distance formula:

\[ D = \sqrt{(3)^2 + (0)^2} \]

### Step 4: Calculate the final distance
Now calculate the square root:

\[ D = \sqrt{9 + 0} = \sqrt{9} = 3 \]

### Conclusion
Thus, the distance between the points \( P \) and \( Q \) is \( 3 \) units.

---