This document outlines a math lesson on calculating distance on the coordinate plane. It includes: - An opening exercise asking students to calculate distances between towns on a map and identify the intersection of roads on the coordinate plane. - Examples of calculating the distance between two points that share an x-coordinate (vertical line segment) and between two points that share a y-coordinate (horizontal line segment). - An exercise asking students to calculate the lengths of several line segments by identifying if they are horizontal or vertical based on shared x- or y-coordinates and computing the absolute value of the differences between the coordinates. - A closing reflection asking students about calculating lengths of non-axis line segments and real-world

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Homework Review Lesson 17

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Monday
Problem Set Lesson 18 &
Crossword
Tuesday Problem Set Lesson 19
Wednesday Study Module 3
Thursday End of Module 3 Assessment
Friday Mod 4 Problem Set Lesson 1

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MODULE 3 Rational Numbers
Topic C: Rational Numbers & the Coordinate Plane
Lesson 18: Distance on the Coordinate Plane
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.

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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?

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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)?

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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)
1­ identify the line
2 ­ identify the distances
3 ­ identify the locations
4 ­ calculate

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Example 3: Length of a Horizontal or Vertical Line Segment that
does Not Lie on an Axis
Find the length of the line segment with endpoints (‐3, 3) and (‐3, ‐5)
What do the endpoints, which are represented by the ordered pairs,
have in common? What does that tell us about the location of the
line segment on the coordinate plane?
Find the length of the line segment by finding the distance between
its endpoints.
1­ identify the line
2 ­ identify the distances
3 ­ identify the locations
4 ­ calculate

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Exercises
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) and (‐3, 9)
b. (2, ‐2) and (‐8, ‐2)
1­ identify the line
2 ­ identify the distances
3 ­ identify the locations
4 ­ calculate
same x­coordinate­vertical line
same y­coordinate­horizontal line

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c. (‐6, ‐6) and (‐6, 1)
d. (‐9,4) and (‐4,4)
e. (0,‐11) and (0, 8)
1­ identify the line
2 ­ identify the distances
3 ­ identify the locations
4 ­ calculate

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Closing
Please take out your exit ticket for Lesson 18, close your
binder, and complete the exit ticket. This will be collected.
§ Why can we find the length of a horizontal or vertical line segment even if it’s not on the x or y ‐axis?
§ Can you think of a real‐world situation where this might be useful?

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