If the distance between the points A(-3, -14) and B(p, -5) is 9 units, then the value of p is:

Options

A. 1
B. -7
C. -3
D. 5

Answer

To solve the problem where the distance between the points A(-3, -14) and B(p, -5) is 9 units, we can follow these steps:

### Step 1: Use the Distance Formula
The distance \( d \) between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In our case, \( A(-3, -14) \) and \( B(p, -5) \).

### Step 2: Substitute the Coordinates into the Formula
Substituting the coordinates of points A and B into the distance formula, we have:
\[ 9 = \sqrt{(p - (-3))^2 + (-5 - (-14))^2} \]
This simplifies to:
\[ 9 = \sqrt{(p + 3)^2 + (9)^2} \]

### Step 3: Square Both Sides to Eliminate the Square Root
To eliminate the square root, we square both sides:
\[ 9^2 = (p + 3)^2 + 9^2 \]
This gives us:
\[ 81 = (p + 3)^2 + 81 \]

### Step 4: Simplify the Equation
Subtract 81 from both sides:
\[ 81 - 81 = (p + 3)^2 \]
This simplifies to:
\[ 0 = (p + 3)^2 \]

### Step 5: Solve for \( p \)
Taking the square root of both sides, we get:
\[ p + 3 = 0 \]
Thus, solving for \( p \):
\[ p = -3 \]

### Final Answer
The value of \( p \) is:
\[ \boxed{-3} \]