Finding Distance Using Absolute Value
Finding Distance Using Absolute Value is a Grade 6 math skill from Big Ideas Math, Course 1, Chapter 6: Integers and the Coordinate Plane. On a number line or coordinate grid, distance between two points sharing the same x- or y-coordinate equals the absolute value of the difference of their varying coordinates. For horizontal points (x₁, y) and (x₂, y): d = |x₂ - x₁|. For vertical points (x, y₁) and (x, y₂): d = |y₂ - y₁|. Example: distance between (-4, 5) and (3, 5) = |3 - (-4)| = |7| = 7 units.
Key Concepts
To find the distance between two points on the same horizontal or vertical line, use the absolute value of the difference of the coordinates that are not the same.
For two points on a horizontal line, $(x 1, y)$ and $(x 2, y)$, the distance is $d = |x 2 x 1|$. For two points on a vertical line, $(x, y 1)$ and $(x, y 2)$, the distance is $d = |y 2 y 1|$.
Common Questions
How do you find distance between two points on a coordinate grid?
For two points on the same horizontal line, subtract the x-coordinates and take the absolute value: d = |x₂ - x₁|. For two points on the same vertical line, subtract the y-coordinates: d = |y₂ - y₁|. Absolute value ensures the answer is positive.
How do you find the distance between (-4, 5) and (3, 5)?
These points share the same y-coordinate (5), so they're on a horizontal line. Distance = |x₂ - x₁| = |3 - (-4)| = |3 + 4| = |7| = 7 units.
Why do you use absolute value for distance?
Distance is always positive, but subtraction can give negative results. Absolute value converts any negative result to positive, guaranteeing that distance is a non-negative number regardless of which coordinate you subtract from which.
How do you find the distance between (2, -1) and (2, -6)?
These points share the same x-coordinate (2), so they're on a vertical line. Distance = |y₂ - y₁| = |-6 - (-1)| = |-6 + 1| = |-5| = 5 units.
When do Grade 6 students learn distance on the coordinate plane?
This skill is in Big Ideas Math, Course 1, Chapter 6: Integers and the Coordinate Plane, which covers all four quadrants of the coordinate grid as part of Grade 6 math.
What is the coordinate plane?
The coordinate plane is a two-dimensional grid formed by two perpendicular number lines: the horizontal x-axis and vertical y-axis. Points are located using (x, y) coordinate pairs, where x shows horizontal position and y shows vertical position.