## Reflection: Advanced Students Partitioning Segments in the Coordinate Plane - Section 6: Extension Task: Centroid as Partitioner

Knowing that the centroid is located 2/3 of the way along the median from a vertex to the midpoint of the opposite side is a very useful fact when solving problems involving points of concurrency (particularly in equilateral triangles when all centroid, orthocenter, circumcenter and incenter coincide). For this reason, I share this useful fact with my students.

Most students are happy just to know the fact and to be able to use it to make problems easier to solve. In fact they would prefer not to know the why and how of it. But I had one student, in particular, this year who would always stay after class and ask "But why is that true?" I designed this extension task for this student and students like him all over the world.

Seriously, though, in retrospect, how nice it would have been to be able to respond to this student's query with a prepared task such as this that would capitalize on his curiosity and challenge him in a way that would spur his growth. Well, next time this scenario occurs, I'll be prepared.

# Partitioning Segments in the Coordinate Plane

Unit 9: Analytic Geometry
Lesson 6 of 7

## Big Idea: 'Howdy Partishner'...In this lesson, students will use analytic geometry to define the coordinates of partitioning points.

Print Lesson
34 teachers like this lesson
Standards:
115 minutes

### Anthony Carruthers

##### Similar Lessons

###### Segments First
Geometry » Introduction to Geometry: Points, Lines, Planes, and Angles
Big Idea: Students will measure, measure, measure to discover properties of segments.
Favorites(13)
Resources(26)
Saratoga Springs, NY
Environment: Suburban