The centroid of a triangle is often called the balancing point of the triangle. It is the point at which the medians of the triangle intersect.

Students used technology to explore the relationship between the vertices of a triangle in the coordinate plane and the vertices of the centroid.

If your students knew the relationship between the vertices of a triangle and the vertices of the centroid, how would you expect them to answer the following question? (I included this question on an end of unit assessment.)

The vertices of a triangle are (a,b–c), (b,c–a), and (c,a–b). Prove that its centroid lies on the x-axis.

A few of my student responses are below.

What learning opportunities could I have provided in class to better prepare my students for this question without just giving them a similar problem?

And so the journey to provide meaningful learning episodes that prepare students to answer questions they haven’t seen before continues …

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howardat58

August 22, 2016 at 4:17 pm

Four points. Or any number of points.

The sum of the y-cordinates is algebraic, not geometrical.nd have

And have you looked at the angle bisectors yet ?