Finding Horizontal and Vertical Side Lengths
Finding horizontal and vertical side lengths on the coordinate plane is a Grade 6 geometry skill in Reveal Math, Course 1. A horizontal segment connects two points with the same y-coordinate; its length is the absolute value of the difference of the x-coordinates. A vertical segment connects two points with the same x-coordinate; its length is the absolute value of the difference of the y-coordinates. For example, from (-3, 4) to (5, 4): length = |5 - (-3)| = 8. Using absolute value handles both positive and negative coordinates correctly. This skill is the basis for finding the perimeter and area of polygons on the coordinate plane.
Key Concepts
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).
Session 2. Finding Horizontal and Vertical Side Lengths.
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.
Common Questions
How do you find the length of a horizontal segment on the coordinate plane?
Find the absolute value of the difference of the x-coordinates (y-coordinates are the same). Length = |x2 - x1|. For points (-2, 3) and (6, 3): |6 - (-2)| = |8| = 8 units.
How do you find the length of a vertical segment on the coordinate plane?
Find the absolute value of the difference of the y-coordinates (x-coordinates are the same). Length = |y2 - y1|. For points (4, -5) and (4, 3): |3 - (-5)| = |8| = 8 units.
Why do you use absolute value when finding segment lengths?
Lengths are always positive. Using absolute value ensures the result is non-negative regardless of which direction the segment runs or whether coordinates are negative.
How do you use coordinate plane side lengths to find the area of a rectangle?
Find the horizontal side length (|x2 - x1|) and vertical side length (|y2 - y1|). Then use A = length x width with these values.
What are common mistakes when finding segment lengths on the coordinate plane?
Subtracting in the wrong order and getting a negative length (which absolute value would fix but students sometimes skip), or using the wrong pair of coordinates (accidentally subtracting a y-value from an x-value).
When do students learn to find side lengths on the coordinate plane?
This skill is introduced in Grade 6 in Reveal Math, Course 1, in the coordinate geometry chapter, building toward finding area and perimeter on the coordinate plane.
Which textbook covers finding horizontal and vertical side lengths?
Reveal Math, Course 1, used in Grade 6, covers coordinate plane side lengths in the geometry chapter.