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Module 3 Lesson 18 Distance on the Coordinate Plane.notebook

March 03, 2014

Homework Review Lesson 17

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Module 3 Lesson 18 Distance on the Coordinate Plane.notebook

March 03, 2014

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Module 3 Lesson 18 Distance on the Coordinate Plane.notebook

March 03, 2014

 MODULE 3 Raonal Numbers
Topic C: Raonal Numbers & the Coordinate Plane
Lesson 18:  Distance on the Coordinate Plane 
Student Outcomes
§
Students compute the length of horizontal and vercal line segments with integer coordinates for endpoints in 
the coordinate plane by counng the number of units between end points and using absolute value. 

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Module 3 Lesson 18 Distance on the Coordinate Plane.notebook

March 03, 2014

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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Module 3 Lesson 18 Distance on the Coordinate Plane.notebook

March 03, 2014

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 locaon in the 
coordinate plane?
Both of their y‐coordinates are zero so each point lies on the x­axis, the horizontal number 
line. 
How did we find the distance between two numbers on the number line?
We calculated the absolute values of the numbers, which told us how far the numbers were 
from zero.  If the numbers were located on opposite sides of zero, then we added their 
absolute values together.  If the numbers were located on the same side of zero, then we 
subtracted their absolute values.
Use the same method to find the distance between  (‐4, 0) and (5,0)

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Module 3 Lesson 18 Distance on the Coordinate Plane.notebook

March 03, 2014

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 locaon in the coordinate plane?

The x‐coordinates of both endpoints are zero so the points lie on the y‐axis, 
the vercal number line.  If its endpoints lie on a vercal number line, then 
the line segment itself must also lie on the vercal line. 
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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Module 3 Lesson 18 Distance on the Coordinate Plane.notebook

March 03, 2014

Example 3:  Length of a Horizontal or Vercal 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 locaon of the 
line segment on the coordinate plane? 

Both endpoints have x‐coordinates of  ‐3 so the points lie 
on the vercal line that intersects the x‐axis at ‐3.  This 
means that the endpoints of the line segment, and thus 
the line segment, lie on a vercal line.
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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Module 3 Lesson 18 Distance on the Coordinate Plane.notebook

March 03, 2014

1­ identify the line
2 ­ identify the distances
3 ­ identify the locations
Exercises

4 ­ calculate

1. Find the lengths of the line segments whose endpoints are given below.  Explain 
how you determined that the line segments are horizontal or vercal.  
a. (‐3, 4) and (‐3, 9)

b. (2, ‐2) and (‐8, ‐2)

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Module 3 Lesson 18 Distance on the Coordinate Plane.notebook

March 03, 2014

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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Module 3 Lesson 18 Distance on the Coordinate Plane.notebook

March 03, 2014

Closing
§

Why can we find the length of a horizontal or vercal line segment even if it’s not on the x or y ‐axis?

§

Can you think of a real‐world situaon where this might be useful?

Please take out your exit ticket for Lesson 18, close your
binder, and complete the exit ticket. This will be collected.

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Module 3 Lesson 18 Distance on the Coordinate Plane.notebook

March 03, 2014

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