Lengths of Segments
Lengths of segments is a Grade 6 math skill in Saxon Math, Course 1 that teaches students to calculate the length of a line segment on a number line or coordinate plane by finding the absolute difference between endpoint coordinates. For a horizontal segment from (2, 3) to (7, 3), the length is |7 − 2| = 5 units. For a vertical segment from (4, 1) to (4, 6), the length is |6 − 1| = 5 units. Students also use rulers and number line scales for segments shown in diagrams. This foundational skill supports perimeter calculation, the distance formula, and coordinate geometry throughout middle school.
Key Concepts
Property The length of $\overline{WX}$ plus the length of $\overline{XY}$ equals the length of $\overline{WY}$.
Examples If $\overline{LM} = 4 \text{ cm}$ and $\overline{MN} = 5 \text{ cm}$, then $\overline{LN} = 4 \text{ cm} + 5 \text{ cm} = 9 \text{ cm}$. If $\overline{AC} = 60 \text{ mm}$ and $\overline{BC} = 26 \text{ mm}$, then $\overline{AB} = 60 \text{ mm} 26 \text{ mm} = 34 \text{ mm}$. If $\overline{WX} = 53 \text{ mm}$ and $\overline{XY} = 35 \text{ mm}$, then $\overline{WY} = 53 \text{ mm} + 35 \text{ mm} = 88 \text{ mm}$.
Explanation Imagine a chocolate bar broken into two pieces. The bar's total length is simply the first piece's length plus the second. This simple rule is super useful for finding a missing segment's length if you know the total length and one of the other parts.
Common Questions
How do you find the length of a horizontal segment on a coordinate plane?
Subtract the smaller x-coordinate from the larger x-coordinate. For a segment from (2, 5) to (9, 5): length = 9 − 2 = 7 units.
How do you find the length of a vertical segment on a coordinate plane?
Subtract the smaller y-coordinate from the larger y-coordinate. For a segment from (3, 1) to (3, 8): length = 8 − 1 = 7 units.
How do you find the length of a segment on a number line?
Find the absolute difference between the two endpoint values. For endpoints at −3 and 5: length = |5 − (−3)| = |5 + 3| = 8 units.
What is a line segment?
A line segment is a part of a line with two definite endpoints. It has a measurable length, unlike a line which extends infinitely in both directions.
How does finding segment lengths relate to perimeter?
Perimeter is the sum of all side lengths of a polygon. Each side is a segment. Finding individual segment lengths from coordinates is the first step in calculating perimeter on the coordinate plane.