### Instruction: Find the distance between the points $(2,2)$ and $(-1,-1)$.### Response: To find the distance between two points, I can use the distance formula, which is based on the Pythagorean theorem.
The distance formula says that the distance $d$ between $(x_1,y_1)$ and $(x_2,y_2)$ is given by $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
In this problem, I have $(x_1,y_1)=(2,2)$ and $(x_2,y_2)=(-1,-1)$, so I can plug these values into the formula.
I get $d=\sqrt{(-1-2)^2+(-1-2)^2}=\sqrt{(-3)^2+(-3)^2}=\sqrt{9+9}=\sqrt{18}$.
I can simplify this by factoring out a $9$ from the square root.
I get $d=\sqrt{9}\sqrt{2}=3\sqrt{2}$.
This is the exact answer, but if I want an approximate decimal answer, I can use a calculator to get $d\approx 4.24$.