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

Answer: (A)

$2\sqrt{13}$ units

Answer 2

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.