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:

Always simplify the square root for exact answers when using the distance formula.

Answer 1

The Correct Option is B

The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the given points \( (1, -3) \) and \( (4, -6) \): \[ d = \sqrt{(4 - 1)^2 + (-6 - (-3))^2} \]
Simplifying the equation: \[ d = \sqrt{(3)^2 + (-3)^2} = \sqrt{9 + 9} = \sqrt{18} \]
Finally, simplifying \( \sqrt{18} \), we get: \[ d = 3\sqrt{2} \]