1. **Problem Statement:** Find the distance between points A and B on a coordinate grid where point B is 2 units right and 2 units up from point A. 2. **Formula Used:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Apply the formula:** Since B is 2 units right and 2 units up from A, the change in x is $\Delta x = 2$ and the change in y is $\Delta y = 2$. 4. Substitute these values: $$d = \sqrt{2^2 + 2^2}$$ 5. Simplify inside the square root: $$d = \sqrt{4 + 4}$$ 6. Add the terms: $$d = \sqrt{8}$$ 7. Simplify the square root: $$d = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$$ 8. **Final answer:** The length of the segment connecting points A and B is $2\sqrt{2}$ units.