Skill: Calculate the distance between two points

The distance between two points is the length of the line segment connecting them. For points $(x_1,y_1)$ and $(x_2,y_2)$, use the distance formula:

$$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

This formula uses the horizontal change, $x_2-x_1$, and the vertical change, $y_2-y_1$.

Example: Find the distance between $A(-2,1)$ and $B(4,9)$.

1. Identify the coordinates:

$$(x_1,y_1)=(-2,1), \qquad (x_2,y_2)=(4,9)$$

2. Substitute into the formula:

$$d=\sqrt{(4-(-2))^2+(9-1)^2}$$

3. Simplify the differences:

$$d=\sqrt{6^2+8^2}$$

4. Square and add:

$$d=\sqrt{36+64}=\sqrt{100}$$

5. Simplify:

$$d=10$$

The distance between $A$ and $B$ is $\boxed{10}$ units. Reversing the order of the points gives the same distance because the differences are squared.