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1.
Lesson 7: Distanceon
theCoordinate Plane Date: 5/21/15 S.30 30 © 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 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
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