Question

Find the distance between the points $ (2, 3) $ and $ (5, 7) $ in the Cartesian plane.

• A. 5
• B. 4
• C. 6
• D. 7

Hint:

Use the distance formula \( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \) to find the straight-line distance between two points in the Cartesian plane.

Answer 1

The Correct Option is A

Given: \[ \text{Point 1} = (2, 3), \quad \text{Point 2} = (5, 7) \] Step 1: Distance Formula
The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Step 2: Calculate Distance
Substitute the coordinates: \[ d = \sqrt{(5 - 2)^2 + (7 - 3)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \] Thus, the distance is: \[ \boxed{5} \]