The distance between the points A (-1,6) and B(2,2) is

Options

A. 6
B. 5
C. 4
D. 2

Answer

To find the distance between the points A (-1, 6) and B (2, 2), we will use the distance formula. The distance formula is given by:

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

Where:
- \( (x_1, y_1) \) are the coordinates of point A
- \( (x_2, y_2) \) are the coordinates of point B

### Step 1: Identify the coordinates
From the problem, we have:
- Point A: \( (x_1, y_1) = (-1, 6) \)
- Point B: \( (x_2, y_2) = (2, 2) \)

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

\[ d = \sqrt{(2 - (-1))^2 + (2 - 6)^2} \]

### Step 3: Simplify the expressions inside the square root
Calculate \( 2 - (-1) \):

\[ 2 - (-1) = 2 + 1 = 3 \]

Calculate \( 2 - 6 \):

\[ 2 - 6 = -4 \]

Now substitute these values back into the formula:

\[ d = \sqrt{(3)^2 + (-4)^2} \]

### Step 4: Calculate the squares
Now calculate the squares:

\[ d = \sqrt{9 + 16} \]

### Step 5: Add the results
Add the results inside the square root:

\[ d = \sqrt{25} \]

### Step 6: Take the square root
Finally, take the square root:

\[ d = 5 \]

Thus, the distance between the points A and B is **5 units**.

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