Question

The distance between the points \( A(3, 4) \) and \( B(-1, -2) \) is:

• A. \(2\sqrt{13}\)
• B. \( 6 \)
• C. \( 7 \)
• D. \( 8 \)

Hint:

When calculating the distance between two points, use the distance formula and ensure you substitute the coordinates correctly. If the result is not an integer, round to the nearest appropriate value.

Answer 1

The Correct Option is A

The distance formula between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Points provided:

• A: \( (3, 4) \)
• B: \( (-1, -2) \)

1. Calculate distance

Substitute the coordinates into the distance formula: \[ d = \sqrt{((-1) - 3)^2 + ((-2) - 4)^2} \] Simplify the terms: \[ d = \sqrt{(-4)^2 + (-6)^2} \] \[ d = \sqrt{16 + 36} = \sqrt{52} \] \[ d = \sqrt{4 \times 13} = 2\sqrt{13} \]

✅ Result:

The calculated distance between \( A(3,4) \) and \( B(-1,-2) \) is \( \boxed{2\sqrt{13}} \).