Find the distance between the pair of points `(5,-12)` and `(9,-9)`.

Options

A. 5
B. 4
C. 12
D. None

Answer

To find the distance between the points \( (5, -12) \) and \( (9, -9) \), 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 \( (x_1, y_1) = (5, -12) \) and \( (x_2, y_2) = (9, -9) \).

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

\[ d = \sqrt{(9 - 5)^2 + (-9 - (-12))^2} \]

### Step 3: Simplify the expressions inside the square root
Calculate \( (9 - 5) \) and \( (-9 - (-12)) \):

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

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

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

### 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 \( (5, -12) \) and \( (9, -9) \) is \( 5 \) units.

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