Skill: Determine horizontal and vertical distances on a coordinate plane

To find a horizontal distance, compare the $x$-coordinates when the two points have the same $y$-coordinate.

$$\text{Horizontal distance}=\lvert x_2-x_1\rvert$$

To find a vertical distance, compare the $y$-coordinates when the two points have the same $x$-coordinate.

$$\text{Vertical distance}=\lvert y_2-y_1\rvert$$

The absolute value symbols $\lvert\ \rvert$ make the distance nonnegative, no matter which direction you move.

Example: Find the horizontal distance from $A(-3,2)$ to $B(4,2)$ and the vertical distance from $B(4,2)$ to $C(4,-5)$.

Step 1: Find the horizontal distance from $A$ to $B$.

The points $A(-3,2)$ and $B(4,2)$ have the same $y$-coordinate, so they form a horizontal segment. Compare their $x$-coordinates:

$$\lvert 4-(-3)\rvert=\lvert 7\rvert=7$$

The horizontal distance is $\boxed{7}$ units.

Step 2: Find the vertical distance from $B$ to $C$.

The points $B(4,2)$ and $C(4,-5)$ have the same $x$-coordinate, so they form a vertical segment. Compare their $y$-coordinates:

$$\lvert -5-2\rvert=\lvert -7\rvert=7$$

The vertical distance is $\boxed{7}$ units.

Even though the vertical segment crosses $0$, its distance is still positive: $7$ units.