Determine horizontal and vertical distances on a coordinate plane

For two points on a coordinate plane, horizontal separation is the absolute difference of their $x$ -coordinates, and vertical separation is the absolute difference of their $y$ -coordinates, measured in coordinate units and interpreted as a nonnegative quantity regardless of quadrant or direction. This reasoning supports analyzing translations and axis-aligned figures; diagonal distance and the distance formula are not included.

Detailed Explanation: Determine horizontal and vertical distances on a coordinate plane

To find the horizontal distance between two points, compare their $x$ -coordinates:

\text{horizontal distance}=\left \vert x_2-x_1\right \vert

To find the vertical distance, compare their $y$ -coordinates:

\text{vertical distance}=\left \vert y_2-y_1\right \vert

The absolute value symbols $\left \vert \right \vert$ make the distance nonnegative, even if the points are in different quadrants or the coordinates are decreasing.

Example

Find the horizontal and vertical distances between $A(-3,4)$ and $B(5,-2)$ .

Step 1: Find the horizontal distance.

Use the $x$ -coordinates, $-3$ and $5$ :

\left \vert 5-(-3)\right \vert =\left \vert 8\right \vert =8

The horizontal distance is 8 coordinate units.

Step 2: Find the vertical distance.

Use the $y$ -coordinates, $4$ and $-2$ :

\left \vert -2-4\right \vert =\left \vert -6\right \vert =6

The vertical distance is 6 coordinate units.

So, the points are 8 units apart horizontally and 6 units apart vertically. These measurements describe movement left or right and up or down; they do not measure the diagonal distance between the points.

Learn by doing: Determine horizontal and vertical distances on a coordinate plane

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Cartesian Grid - Distance Between Coordinates (Straight)

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