1. Lesson 7: Distanceon theCoordinate Plane
Date: 5/21/15 S.30
30
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•5Lesson 7
Lesson 7: Distance on the Coordinate Plane
Classwork
Example 1
Determine the lengths of the given linesegments by determining the distancebetween the two endpoints.
Line
Segment
Point Point Distance Proof
𝐴𝐵̅̅̅̅
𝐵𝐶̅̅̅̅
𝐶𝐷̅̅̅̅
𝐵𝐷̅̅̅̅
𝐷𝐸̅̅̅̅
𝐸𝐹̅̅̅̅
𝐹𝐺̅̅̅̅
𝐸𝐺̅̅̅̅
𝐺𝐴̅̅̅̅
𝐹𝐴̅̅̅̅
𝐸𝐴̅̅̅̅

2. Lesson 7: Distanceon theCoordinate Plane
Date: 5/21/15 S.31
31
© 2014 Common Core, Inc. Some rightsreserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•5Lesson 7
Exercises
Complete the tableusingthe diagramon the coordinateplane.
Line
Segment
Point Point Distance Proof
𝑩𝑰̅̅̅̅
𝑩𝑯̅̅̅̅̅
𝑩𝑬̅̅̅̅
𝑮𝑯̅̅̅̅̅
𝑯𝑪̅̅̅̅
𝑮𝑪̅̅̅̅
𝑪𝑫̅̅̅̅
𝑭𝑮̅̅̅̅
𝑮𝑨̅̅̅̅
𝑨𝑭̅̅̅̅

3. Lesson 7: Distanceon theCoordinate Plane
Date: 5/21/15 S.32
32
© 2014 Common Core, Inc. Some rightsreserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•5Lesson 7
Extension
For each problem below, write the coordinates of two points that are 5 units apartwith the segment connecting these
points havingthe followingcharacteristic:
a. The segment is vertical.
b. The segment intersects the 𝑥-axis.
c. The segment intersects the 𝑦-axis.
d. The segment is vertical and lies abovethe 𝑥-axis.

4. Lesson 7: Distanceon theCoordinate Plane
Date: 5/21/15 S.33
33
© 2014 Common Core, Inc. Some rightsreserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•5Lesson 7
Problem Set
1. Given the pairs of points,determine whether the segment that joins them will be horizontal,vertical ,or neither.
a. 𝑋(3, 5) and 𝑌(−2, 5)
b. 𝑀(−4, 9) and 𝑁(4,−9)
c. 𝐸(−7, 1) and 𝐹(−7, 4)
2. Complete the tableusingabsolutevalueto determine the lengths of the linesegments.
Line Segment Point Point Distance Proof
𝐴𝐵̅̅̅̅ (−𝟑, 𝟓) (𝟕, 𝟓)
𝐶𝐷̅̅̅̅ (𝟏, −𝟑) (−𝟔, −𝟑)
𝐸𝐹̅̅̅̅ (𝟐, −𝟗) (𝟐, −𝟑)
𝐺𝐻̅̅̅̅ (𝟔, 𝟏) (𝟔, 𝟏𝟔)
𝐽𝐾̅̅̅ (−𝟑, 𝟎) (−𝟑, 𝟏𝟐)
3. Complete the tableusing the diagramand absolutevalueto determine the lengths of the linesegments.
Line
Segment
Point Point Distance Proof
𝐴𝐵̅̅̅̅
𝐵𝐶̅̅̅̅
𝐶𝐷̅̅̅̅
𝐷𝐸̅̅̅̅
𝐸𝐹̅̅̅̅
𝐹𝐴̅̅̅̅

5. Lesson 7: Distanceon theCoordinate Plane
Date: 5/21/15 S.34
34
© 2014 Common Core, Inc. Some rightsreserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•5Lesson 7
4. Complete the tableusingthe diagramand absolutevalueto determine the lengths of the linesegments.
5. Name two points in different quadrants thatform a vertical linesegment that is 8 units in length.
6. Name two points in the same quadrantthat form a horizontal linesegment that is 5 units in length.
Line
Segment
Point Point Distance Proof
𝐴𝐵̅̅̅̅
𝐶𝐺̅̅̅̅
𝐶𝐹̅̅̅̅
𝐺𝐹̅̅̅̅
𝐷𝐻̅̅̅̅
𝐷𝐸̅̅̅̅
𝐻𝐽̅̅̅̅
𝐾𝐿̅̅̅̅