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

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

Given:

• Point A: \( (3, 4) \)
• Point B: \( (-1, -2) \)

Step 1: Apply the distance formula

Substitute the values of \( x_1, y_1, x_2, \) and \( y_2 \): \[ d = \sqrt{((-1) - 3)^2 + ((-2) - 4)^2} \] Simplifying the terms inside the parentheses: \[ d = \sqrt{(-4)^2 + (-6)^2} \] \[ d = \sqrt{16 + 36} = \sqrt{52} \] \[ d = \sqrt{4 \times 13} = 2\sqrt{13} \]

✅ Final Answer:

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