### Instruction: Find the distance between the points $(2,2)$ and $(-1,-1)$.### Response: I need to find the distance between two points in the coordinate plane, so I can use the distance formula.
The distance formula is $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of the two points.
I can label $(2,2)$ as $(x_1,y_1)$ and $(-1,-1)$ as $(x_2,y_2)$, or vice versa.
It doesn't matter which one is which, because the distance formula is symmetric.
Plugging in the coordinates into the formula, I get $d = \sqrt{(-1-2)^2+(-1-2)^2}$.
Simplifying the expression inside the square root, I get $d = \sqrt{(-3)^2+(-3)^2}$.
Squaring the negative numbers, I get $d = \sqrt{9+9}$.
Adding the numbers, I get $d = \sqrt{18}$.
I can simplify the square root by factoring out a perfect square.
I notice that $18 = 9 \times 2$, and $9$ is a perfect square.
So I can rewrite $d = \sqrt{9 \times 2}$ as $d = \sqrt{9} \times \sqrt{2}$.
Taking the square root of $9$, I get $d = 3 \times \sqrt{2}$.