Question

The distance between the points $(2,3)$ and $(4,1)$ will be:

• A. $4$
• B. $2$
• C. $2\sqrt{2}$
• D. $\sqrt{2}$

Hint:

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

Answer 1

The Correct Option is C

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

Step 2: Substitute values
Points are $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(4,1)$.
\[ d = \sqrt{(4-2)^2 + (1-3)^2} \] \[ = \sqrt{(2)^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8} \]

Step 3: Simplify
\[ \sqrt{8} = 2\sqrt{2} \] \[ \boxed{d = 2\sqrt{2}} \]