Question

Distance between two points \( (2, 3) \) and \( (4, 1) \) will be:

• A. 2
• B. \( 2\sqrt{3} \)
• C. \( 2\sqrt{2} \)
• D. 3

Hint:

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

Answer 1

The Correct Option is C

The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] For the points \( (2, 3) \) and \( (4, 1) \), we have: - \( x_1 = 2 \) - \( y_1 = 3 \) - \( x_2 = 4 \) - \( y_2 = 1 \) Substitute these values into the distance formula: \[ d = \sqrt{(4 - 2)^2 + (1 - 3)^2} = \sqrt{2^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \]
Step 1: Conclusion.
Therefore, the distance between the two points is \( 2\sqrt{2} \).