Question

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

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

Hint:

The distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] is used to find the distance between two points.

Answer 1

The Correct Option is B

The distance formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting \( (x_1, y_1) = (7, -4) \) and \( (x_2, y_2) = (-5, 1) \):
\[ d = \sqrt{(-5 - 7)^2 + (1 + 4)^2} \] \[ = \sqrt{(-12)^2 + (5)^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \]