Lesson 5: Find Distances on the Coordinate Plane

Session 2. Finding Horizontal and Vertical Side Lengths

Property

To find the length of a side that is perfectly horizontal or vertical, you can either count the grid spaces between the points or find the difference between their coordinates:

• Horizontal lines: Subtract the x-coordinates (the y-coordinates stay the same).
• Vertical lines: Subtract the y-coordinates (the x-coordinates stay the same).

Examples

• The distance between (3, 6) and (10, 6) is a horizontal line. The length is 10 - 3 = 7 units.
• The distance between (4, 2) and (4, 9) is a vertical line. The length is 9 - 2 = 7 units.
• A rectangle has vertices at (1, 1), (6, 1), (6, 5), and (1, 5). Its width (horizontal) is 6 - 1 = 5 units, and its height (vertical) is 5 - 1 = 4 units.

Property

The distance $d$ between two points on a horizontal or vertical line is found using their differing coordinates, $a$ and $b$:

• If the points are on opposite sides of an axis, add their absolute values: $d = |a| + |b|$.
• If the points are on the same side of an axis, subtract the smaller absolute value from the larger: $d = |\text{larger absolute value}| - |\text{smaller absolute value}|$.

Examples