# Distance on the Coordinate Plane

Videos and solutions to help Grade 6 students learn how compute the length of horizontal and vertical line segments on the coordinate plane.

### New York State Common Core Math Grade 6, Module 3, Lesson 18

Worksheets for Grade 6

Lesson 18 Student Outcomes

Students compute the length of horizontal and vertical line segments with integer coordinates for endpoints in the coordinate plane by counting the number of units between end points and using absolute value.

Opening Exercise

Four friends are touring on motorcycles. They come to an intersection of two roads ;the road they are on continues straight, and the other is perpendicular to it. The sign at the intersection shows the distances to several towns. Draw a map/diagram of the roads and use it and the information on the sign to answer the following questions:

What is the distance between Albertsville and Dewey Falls?
What is the distance between Blossville and Cheyenne?
On the coordinate plane, what represents the intersection of the two roads?

Example 1: The Distance Between Points on an Axis

What is the distance between (-4, 0) and (5, 0)?

What do the ordered pairs have in common and what does that mean about their location in the coordinate plane?
How did we find the distance between two numbers on the number line?
Use the same method to find the distance between (-4, 0) and (5, 0).

Example 2: The Length of a Line Segment on an Axis

What is the length of the line segment with endpoints (0, -6) and (0, 11)?

What do the ordered pairs of the endpoints have in common and what does that mean about the line segment’s location in the coordinate plane?

Find the length of the line segment described by finding the distance between its endpoints (0, -6) and (0, 11)?

Find the length of the line segment by finding the distance between its endpoints (-3, 3) and (-3, -5)

Exercise 1

1. Find the lengths of the line segments whose endpoints are given below. Explain how you determined that the line segments are horizontal or vertical.
a) (-3, 4), (-3, 9)
b) (2, -2), (-8, -2)
c) (-6, -6), (-6, 1)
d) (-9, 3), (-4, 4)
e) (0,-11), (0, 8)

Lesson Summary

To find the distance between points that lie on the same horizontal line or on the same vertical line, we can use the same strategy that we used to find the distance between points on the number line.

Lesson 18 Distance in the Coordinate Plane.

Lesson 18 Exit Ticket

Determine whether each given pair of endpoints lies on the same horizontal or vertical line. If so, find the length of the line segment that joins the pair of points. If not, explain how you know the points are not on the same horizontal or vertical line.
a. (0, -2) and (0, 9)
b. (11, 4) and (2, 11)
c. (3, -8) and (3, -1)
d. (-4, -4) and (5, -4)

Problem Set

1. Find the length of the line segment with end points (7,2) and (-4,2), and explain how you arrived at your solution.
2. Sarah and Jamal were learning partners in math class and were working independently. They each started at the point (-2,5) and moved 3 units vertically in the plane. Each student arrived at a different end point. How is this possible? Explain and list the two different end points.
3. The length of a line segment is 13 units. One end point of the line segment is (-3,7). Find four points that could be the other end points of the line segment.

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