Learn on PengiPengi Math (Grade 6)Chapter 5: Coordinate Plane & Graphs

Lesson 2: Horizontal & Vertical Distance on the Plane

In this Grade 6 Pengi Math lesson from Chapter 5, students learn to calculate horizontal and vertical distances between two points on the coordinate plane using absolute differences: d = |x2 − x1| for horizontal segments and d = |y2 − y1| for vertical segments. Students practice identifying when points share the same x- or y-coordinate and apply same-side versus opposite-side reasoning to solve distance problems with labeled units.

Section 1

Calculate Horizontal and Vertical Distance

Property

The distance $d$ between two points on a horizontal or vertical line is found using their differing coordinates, $a$ and $b$ :

If the points are on opposite sides of an axis, add their absolute values: $d = |a| + |b|$ .
If the points are on the same side of an axis, subtract the smaller absolute value from the larger: $d = |\text{larger absolute value}| - |\text{smaller absolute value}|$ .

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 $d = |y_2 - y_1|$ .

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Calculate Horizontal and Vertical Distance

Property

The distance $d$ between two points on a horizontal or vertical line is found using their differing coordinates, $a$ and $b$ :

If the points are on opposite sides of an axis, add their absolute values: $d = |a| + |b|$ .
If the points are on the same side of an axis, subtract the smaller absolute value from the larger: $d = |\text{larger absolute value}| - |\text{smaller absolute value}|$ .

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 $d = |y_2 - y_1|$ .

Overview

Lesson overview

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

Overview

Section 1

Calculate Horizontal and Vertical Distance

Property

The distance $d$ between two points on a horizontal or vertical line is found using their differing coordinates, $a$ and $b$ :

If the points are on opposite sides of an axis, add their absolute values: $d = |a| + |b|$ .
If the points are on the same side of an axis, subtract the smaller absolute value from the larger: $d = |\text{larger absolute value}| - |\text{smaller absolute value}|$ .

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 $d = |y_2 - y_1|$ .