Page 140 - IM_FL_Geometry_Print Sample

Student Response
Answers vary. Sample response: I would swim perpendicular to the shore line because that seems to be the shortest path.
Activity Synthesis
The purpose of discussion is to clarify the concept of the distance between a point and a line. There are many possible segments that can connect a point to a line, all with di erent lengths, but the distance between a point and a line is understood as the length of the shortest path between them.
Ask 1 or 2 students to explain their reasoning about which path they would take. Ask students,
• “There are many, many possible paths from your location at point to the shore. There are many possible distances between point and line . If someone asks how far away you are from the shore, what do they mean precisely?” (They are asking for the shortest possible distance between point and line .)
7.2 Right On Point
15 minutes
The purpose of this activity is to prove that the shortest distance between a point and a line is the length of the path between the point and line that is perpendicular to the line. Students have reasoned about this informally in the warm-up, so this activity gives students the opportunity to use mathematics to construct viable arguments and critique the reasoning of others (MP3).
Instructional Routines
• Think pair share
What: Students have quiet time to think about a problem and work on it individually, and then time to share their response or their progress with a partner. Once these partner conversations have taken place, some students are selected to share their thoughts with the class.
Unit 7
Lesson 7: Tangent Lines 67