Question

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

• A. $2$
• B. $2\sqrt{2}$
• C. $2\sqrt{3}$
• D. $12$

Hint:

Always use the distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ when finding the distance between two points in coordinate geometry.

Answer 1

The Correct Option is B

Step 1: Recall the distance formula
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Step 2: Substitute the given points
Here $(x_1,y_1) = (2,3)$ and $(x_2,y_2) = (4,1)$.
\[ d = \sqrt{(4-2)^2 + (1-3)^2} \]

Step 3: Simplify
\[ = \sqrt{(2)^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8} \] \[ = 2\sqrt{2} \]

Step 4: Conclusion
The distance between the two points is: \[ \boxed{2\sqrt{2}} \]