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

Problem:
We are given two points in the coordinate plane:
- Point A: \( (2, -3) \)
- Point B: \( (-2, 3) \)
We are to find the distance between these two points.

Step 1: Use the distance formula
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here,
\(x_1 = 2\), \(y_1 = -3\)
\(x_2 = -2\), \(y_2 = 3\)

Step 2: Substitute values into the formula
\[ d = \sqrt{(-2 - 2)^2 + (3 - (-3))^2} = \sqrt{(-4)^2 + (6)^2} = \sqrt{16 + 36} = \sqrt{52} \]

Step 3: Simplify the square root
\[ \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13} \]

Final Answer:
The distance between the points is \(2\sqrt{13}\) units.