Question

The distance between the points \( (7, -4) \) and \( (-5, 1) \) is:

• A. \( 12 \)
• B. \( 13 \)
• C. \( 11 \)
• D. \( 5 \)

Hint:

The distance formula is based on the Pythagorean theorem.

Answer 1

The Correct Option is B

Step 1: Use the distance formula The distance 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 2: Substitute values Given points: \( (7, -4) \) and \( (-5, 1) \): \[ d = \sqrt{(-5 - 7)^2 + (1 - (-4))^2} \] \[ = \sqrt{(-12)^2 + (5)^2} \] \[ = \sqrt{144 + 25} \] \[ = \sqrt{169} \] \[ = 13 \] Thus, the correct answer is \( 13 \).