1. **Stating the problem:** We are asked to find the formula for the distance between two points $A(x_1, y_1)$ and $B(x_2, y_2)$. 2. **Formula used:** The distance between two points in a plane is given by the distance formula derived from the Pythagorean theorem: $$AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Explanation:** - The difference in the $x$-coordinates is $x_2 - x_1$. - The difference in the $y$-coordinates is $y_2 - y_1$. - Squaring these differences and adding them gives the square of the distance. - Taking the square root gives the actual distance. 4. **Checking the options:** - Option ក: $AB = \sqrt{(x_2 - x_1) + (y_2 - y_1)}$ (incorrect, no squares inside root) - Option ខ: $AB = \sqrt{(x_2 - x_1)^2 \cdot (y_2 - y_1)^2}$ (incorrect, multiplication inside root) - Option គ: $AB = (x_2 - x_1)^2 + (y_2 - y_1)^2$ (incorrect, missing square root) - Option ឃ: $AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ (correct) **Final answer:** Option ឃ