Question

The distance between the points \( (1,-3) \) and \( (4,-6) \) is:

• A. \( 2\sqrt{3} \)
• B. \( 3\sqrt{2} \)
• C. \( 9 \)
• D. \( 6 \)

Hint:

For two points \( (x_1, y_1) \) and \( (x_2, y_2) \), the Euclidean distance is: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. \]

Answer 1

The Correct Option is B

Using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Given points:
\[ A(1,-3) \quad \text{and} \quad B(4,-6). \] Substituting values:
\[ d = \sqrt{(4 - 1)^2 + (-6 + 3)^2} \] \[ = \sqrt{(3)^2 + (-3)^2} \] \[ = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}. \]