Question

If the distance between the points (4, p) and (1, 0) is 5, then p is equal to :

• A. \( \pm 4 \)
• B. 4
• C. - 4
• D. 0

Hint:

Always remember to include both positive and negative results when solving for a squared variable unless a geometric constraint (like a distance or height) is mentioned for the variable itself.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The distance between two points in a 2D plane is found using the distance formula derived from the Pythagorean theorem.
Step 2: Key Formula or Approach:
Distance \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Step 3: Detailed Explanation:
Points: \( (4, p) \) and \( (1, 0) \). Distance \( d = 5 \).
\[ \sqrt{(1 - 4)^2 + (0 - p)^2} = 5 \]
Square both sides to eliminate the square root:
\[ (-3)^2 + (-p)^2 = 5^2 \]
\[ 9 + p^2 = 25 \]
\[ p^2 = 25 - 9 \]
\[ p^2 = 16 \]
\[ p = \pm \sqrt{16} \]
\[ p = \pm 4 \]
Step 4: Final Answer:
The value of \( p \) is \( \pm 4 \).