Skill: Determine the distance between two points

The distance between two points is the length of the line segment joining them. Use the distance formula:

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

This formula comes from the Pythagorean theorem: the horizontal difference and vertical difference form the two legs of a right triangle.

Example: Find the distance between $A(-2,3)$ and $B(4,-4)$.

1. Identify the coordinates:

$$(x_1,y_1)=(-2,3), \qquad (x_2,y_2)=(4,-4)$$

2. Find the horizontal and vertical differences:

$$x_2-x_1=4-(-2)=6$$ $$y_2-y_1=-4-3=-7$$

3. Substitute into the distance formula:

$$d=\sqrt{6^2+(-7)^2}$$

4. Simplify:

$$d=\sqrt{36+49}=\sqrt{85}$$

Therefore, the exact distance is

$$\boxed{\sqrt{85}\text{ units}}$$

As a decimal, this is approximately

$$\boxed{9.22\text{ units}}$$

The order of the points does not matter. Reversing them changes the signs of the differences, but squaring makes the final distance the same.