1. The problem is to find the distance given by the formula $$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ which calculates the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ on a coordinate plane. 2. For the first problem, calculate $$\sqrt{(-4 + 1)^2 + (1 - 6)^2}$$. 3. Simplify inside the parentheses: $$-4 + 1 = -3$$ $$1 - 6 = -5$$ 4. Substitute back: $$\sqrt{(-3)^2 + (-5)^2} = \sqrt{9 + 25}$$ 5. Add the squares: $$\sqrt{34}$$ 6. The distance is $$\sqrt{34}$$, which is approximately 5.83. This is the distance between the points involved in the first expression.