Applying Absolute Value to Find Distance Between Two Points
Applying Absolute Value to Find Distance Between Two Points is a Grade 6 math skill from Big Ideas Math, Course 1, Chapter 6. Students use the formula D = |a - b| to find the distance between any two values on a number line, regardless of sign. This handles real-world scenarios like finding the vertical distance between a submarine at -250 m and a helicopter at 400 m: |400 - (-250)| = |650| = 650 m. Because distance is always non-negative, absolute value guarantees the answer is positive regardless of subtraction order.
Key Concepts
To find the distance, $D$, between two numbers, $a$ and $b$, on a number line, calculate the absolute value of their difference: $$D = |a b|$$.
Common Questions
How do you find the distance between two integers?
Use the formula D = |a - b|. Subtract one value from the other and take the absolute value. The order doesn't matter: |5 - (-12)| = |17| = 17, and |(-12) - 5| = |-17| = 17. Both give the same distance.
What is absolute value?
Absolute value is the distance of a number from zero on the number line, always expressed as a non-negative number. |7| = 7 and |-7| = 7, because both 7 and -7 are 7 units from zero.
How do you find the distance between a submarine and a helicopter?
If a submarine is at -250 m and a helicopter is at 400 m, the distance is |400 - (-250)| = |400 + 250| = |650| = 650 meters.
Why does order not matter when finding distance?
Because absolute value makes the result positive regardless. |5 - (-12)| = |17| = 17, and |(-12) - 5| = |-17| = 17. Both give 17, confirming that distance between two points is always positive and order-independent.
When do Grade 6 students learn this skill?
This skill is covered in Big Ideas Math, Course 1, Chapter 6: Integers and the Coordinate Plane, as part of Grade 6 math's work with integers and the number line.
What are real-world uses of absolute value distance?
Real-world applications include temperature change (from -12°F to 5°F is a change of 17°F), elevation differences (from -250 m to 400 m is 650 m), financial changes (from -$50 to $30 is a swing of $80), and sports statistics like net scoring changes.