Question

The distance between the points \( (4, 3, 7) \) and \( (1, -1, -5) \) is:

• A. \( 13 \)
• B. \( 15 \)
• C. \( 12 \)
• D. \( 5 \)

Hint:

The distance between points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \) is given by: \[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \] Always square differences and then take the square root.

Answer 1

The Correct Option is B

Step 1: Use the distance formula between two points in 3D space: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \] Step 2: Substitute the coordinates: \[ d = \sqrt{(1 - 4)^2 + (-1 - 3)^2 + (-5 - 7)^2} = \sqrt{(-3)^2 + (-4)^2 + (-12)^2} \] \[ = \sqrt{9 + 16 + 144} = \sqrt{169} = 13 \] Wait — answer looks like 13, which is option (A). Let me double-check. --- Correction: Distance is \( 13 \), so correct answer is (A). --- Final Answer: \( \boxed{13} \)