Question

The distance between the points \((2, -3)\) and \((-2, 3)\) is:

• A. \(2\sqrt{13}\) units
• B. \(5\) units
• C. \(13\sqrt{2}\) units
• D. \(10\) units

Answer 1

The Correct Option is A

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 \((x_1, y_1) = (2, -3)\) and \((x_2, y_2) = (-2, 3)\):

\[ d = \sqrt{(-2 - 2)^2 + (3 - (-3))^2} \]

\[ d = \sqrt{(-4)^2 + (6)^2} = \sqrt{16 + 36} = \sqrt{52} = 2\sqrt{13} \]

Thus, the distance is 5 units.