Learn on PengiReveal Math, Course 1Module 4: Integers, Rational Numbers, and the Coordinate Plane

4-7 Absolute Value and Distance

In this Grade 6 lesson from Reveal Math Course 1, Module 4, students learn how to use absolute value to find horizontal and vertical distances between points on the coordinate plane. They practice identifying whether two points share the same x- or y-coordinate, then apply the rules of subtracting absolute values for points in the same quadrant and adding absolute values for points in different quadrants. Examples work with integers, fractions, and decimals to build fluency across a range of coordinate pairs.

Section 1

Identify Horizontal and Vertical Lines

Property

Horizontal Line: A line parallel to the $x$ -axis with an equation of the form $y = b$ . The distance from this line to the $x$ -axis is $|b|$ .
Vertical Line: A line parallel to the $y$ -axis with an equation of the form $x = a$ . The distance from this line to the $y$ -axis is $|a|$ .

Examples

Section 2

Finding Distance Using Absolute Value

Property

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 $d = |y_2 - y_1|$ .

Section 3

Solve Real-World Distance Problems on a Coordinate Grid

Property

To solve real-world distance problems on a coordinate grid:

Identify the coordinates of the two locations.
Determine if the path is horizontal (same $y$ -coordinates) or vertical (same $x$ -coordinates).
Calculate the grid distance $d$ using absolute values:
- Same quadrant (same signs): Subtract the absolute values.
- Different quadrants (different signs): Add the absolute values.
Multiply by the given scale factor, if applicable:

\text{Actual Distance} = d \times \text{Scale}

Examples

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Module 4: Integers, Rational Numbers, and the Coordinate Plane

Back to Reveal Math, Course 1

Lesson 1
4-1 Represent Integers
Learn Practice
Lesson 2
4-2 Opposites and Absolute Value
Learn Practice
Lesson 3
4-3 Compare and Order Integers
Learn Practice
Lesson 4
4-4 Rational Numbers
Learn Practice
Lesson 5
4-5 The Coordinate Plane
Learn Practice
Lesson 6
4-6 Graph Reflections of Points
Learn Practice
Lesson 7Current
4-7 Absolute Value and Distance
Learn Practice

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Identify Horizontal and Vertical Lines

Property

Horizontal Line: A line parallel to the $x$ -axis with an equation of the form $y = b$ . The distance from this line to the $x$ -axis is $|b|$ .
Vertical Line: A line parallel to the $y$ -axis with an equation of the form $x = a$ . The distance from this line to the $y$ -axis is $|a|$ .

Examples

Section 2

Finding Distance Using Absolute Value

Property

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 $d = |y_2 - y_1|$ .

Section 3

Solve Real-World Distance Problems on a Coordinate Grid

Property

To solve real-world distance problems on a coordinate grid:

Identify the coordinates of the two locations.
Determine if the path is horizontal (same $y$ -coordinates) or vertical (same $x$ -coordinates).
Calculate the grid distance $d$ using absolute values:
- Same quadrant (same signs): Subtract the absolute values.
- Different quadrants (different signs): Add the absolute values.
Multiply by the given scale factor, if applicable:

\text{Actual Distance} = d \times \text{Scale}

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Module 4: Integers, Rational Numbers, and the Coordinate Plane

Back to Reveal Math, Course 1

Lesson 1
4-1 Represent Integers
Learn Practice
Lesson 2
4-2 Opposites and Absolute Value
Learn Practice
Lesson 3
4-3 Compare and Order Integers
Learn Practice
Lesson 4
4-4 Rational Numbers
Learn Practice
Lesson 5
4-5 The Coordinate Plane
Learn Practice
Lesson 6
4-6 Graph Reflections of Points
Learn Practice
Lesson 7Current
4-7 Absolute Value and Distance
Learn Practice

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Identify Horizontal and Vertical Lines

Property

Horizontal Line: A line parallel to the $x$ -axis with an equation of the form $y = b$ . The distance from this line to the $x$ -axis is $|b|$ .
Vertical Line: A line parallel to the $y$ -axis with an equation of the form $x = a$ . The distance from this line to the $y$ -axis is $|a|$ .

Examples

Section 2

Finding Distance Using Absolute Value

Property

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 $d = |y_2 - y_1|$ .

Section 3

Solve Real-World Distance Problems on a Coordinate Grid

Property

To solve real-world distance problems on a coordinate grid:

Identify the coordinates of the two locations.
Determine if the path is horizontal (same $y$ -coordinates) or vertical (same $x$ -coordinates).
Calculate the grid distance $d$ using absolute values:
- Same quadrant (same signs): Subtract the absolute values.
- Different quadrants (different signs): Add the absolute values.
Multiply by the given scale factor, if applicable:

\text{Actual Distance} = d \times \text{Scale}

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Module 4: Integers, Rational Numbers, and the Coordinate Plane

Back to Reveal Math, Course 1

Lesson 1
4-1 Represent Integers
Learn Practice
Lesson 2
4-2 Opposites and Absolute Value
Learn Practice
Lesson 3
4-3 Compare and Order Integers
Learn Practice
Lesson 4
4-4 Rational Numbers
Learn Practice
Lesson 5
4-5 The Coordinate Plane
Learn Practice
Lesson 6
4-6 Graph Reflections of Points
Learn Practice
Lesson 7Current
4-7 Absolute Value and Distance
Learn Practice

4-7 Absolute Value and Distance

Property

Examples

Property

Property

Examples

Module 4: Integers, Rational Numbers, and the Coordinate Plane

4-1 Represent Integers

4-2 Opposites and Absolute Value

4-3 Compare and Order Integers

4-4 Rational Numbers

4-5 The Coordinate Plane

4-6 Graph Reflections of Points

4-7 Absolute Value and Distance

Lesson overview

Property

Examples

Property

Property

Examples

Module 4: Integers, Rational Numbers, and the Coordinate Plane

4-1 Represent Integers

4-2 Opposites and Absolute Value

4-3 Compare and Order Integers

4-4 Rational Numbers

4-5 The Coordinate Plane

4-6 Graph Reflections of Points

4-7 Absolute Value and Distance

4-1 Represent Integers

4-2 Opposites and Absolute Value

4-3 Compare and Order Integers

4-4 Rational Numbers

4-5 The Coordinate Plane

4-6 Graph Reflections of Points

4-7 Absolute Value and Distance