Determine horizontal and vertical distances on a coordinate plane

Horizontal and vertical distance on a coordinate plane is determined by comparing one coordinate at a time: points with the same $y$ -coordinate have horizontal distance $|x_2-x_1|$ , and points with the same $x$ -coordinate have vertical distance $|y_2-y_1|$ . Distance is nonnegative regardless of direction, including across zero, and this understanding supports analyzing translations and other coordinate transformations; diagonal distances and the distance formula are not included.

Detailed Explanation: 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.

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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Determine horizontal and vertical distances on a coordinate plane

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

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

Practice with unlimited practice problems

Practice:

Cartesian Grid - Distance Between Coordinates (Straight)