Skill: Find horizontal distance between points

To find the horizontal distance between two points, make sure they have the same $y$-coordinate. Then subtract their $x$-coordinates and take the absolute value:

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

The absolute value makes the distance positive, no matter which point comes first.

Example: Find the horizontal distance between $A(-4, 3)$ and $B(5, 3)$.

1. Check the $y$-coordinates: both are $3$, so the points are on the same horizontal line.
2. Identify the $x$-coordinates: $x_1=-4$ and $x_2=5$.
3. Subtract and use absolute value:

$$\lvert x_2-x_1\rvert=\lvert 5-(-4)\rvert$$

4. Simplify:

$$\lvert 5+4\rvert=\lvert 9\rvert=9$$

The horizontal distance between the points is $9$ units.