How far apart are these points?

In this lesson you will learn to use absolute value to find

distances between points with the same x and y value by using a coordinate plane.

Let’s Review The Coordinate Plane

(5,3)

x value y value

(-2,-3)

Let’s Review

|-3| = 3

|3| = 3

Absolute Value: The distance a number is from zero on

the number line.

A Common Mistake

Begin by moving along the y-axis first, and then along the x-axis when finding an ordered pair.

(6,4)

A Common Mistake

Returning to the origin after plotting the x value, and then moving on the y-axis.

(6,4)

Core Lesson

A (6,4)

B (6,0)

|4 – 0| = |4| = 4

OR

|0 – 4| = |-4| = 4

A

B

4 units

Core Lesson

C (5,-6)

D (0,-6)

|5 – 0| = |5| = 5 OR

|0 – 5| = |-5| = 5C

D

5 units

Core Lesson

E (0,4)

F (6,4)

FE

|0-6|= |-6| = 6

OR

|6 – 0| = |6| = 6

6 units

In this lesson you have learned to use absolute value to find

distances between points with the same x and y value by using a coordinate plane.

Guided Practice

What is the distance between the two coordinate pairs A (2,-3) and B (0,-3)? Use absolute value and the coordinate plane to solve the problem.

Guided Practice

What is the distance between the two coordinate pairs C (-5,0) and D (-5,-9)? Use absolute value and the coordinate plane to solve the problem.

Extension Activities

Dice Challenge:

1. Roll two dice and use the numbers as the x and y values in an ordered pair. Plot the point on a coordinate plane.

2. Create a point on the x or y-axis that creates a line with your original point.

3. Find the distance between the two points.

Extension Activities

Human Coordinate Plane:

Create a large coordinate plane on the classroom floor using masking tape.

Have one person stand at a point on either the x or y-axis.

Have another person stand on the coordinate plane at a point that shares either the x or y value as the first person.

Have the class find the distance between the two points.

Quick Quiz

Which of the following coordinate pairs has a distance that is 8 units long?

a. (0,-4) (-4, -4)

b. (-3,6) (-3, 0)

c. (0,-5) (8, -5)

Quick Quiz

Which of the following coordinate pairs has an absolute value of -4?

a. (0,-4) (-4, -4)

b. (-3,6) (-3, 0)

c. (0,-5) (8, -5)