The center of mass, also called the center of gravity, is the point where the weight of an object is focused. It is the point of balance of an object.
In a triangle, the center of mass is called the centroid. The centroid is found by drawing the three medians of the triangle. A median of a triangle is a segment that joins a vertex and the midpoint of the side opposite the vertex. The centroid of the triangle is the intersection point of the medians.
For this assignment you will need to use geogebra for your constructions.
Questions:
1) At geogebra, construct a triangle with vertices J, K, and L. Draw and label the three midpoints A, B and C. Draw the three medians.
2) Through geogebra, find the tool to calculate the length of a segment. Find the length of each median. then find the distance from each vertex to the centroid. Round your answers to the nearest tenth of a centimeter.
3) Use your results from exercise 2 to make a conjecture about how the distance from a vertex to the centroid is related to the distance from that vertex to the midpoint of the opposite side.
4) Points W, P , and Y are the midpoints of EF, FG, and GE, r
espectively. Use the triangle to verify the conjecture that you made in exercise 3.
espectively. Use the triangle to verify the conjecture that you made in exercise 3.
Ms. Saatkamp, what do you mean by "make a conjecture" in number 3? Do you want us to compare both distances, make some kind of conclusion?
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