Investigating the Centroid using Transformations

• using the polygon tool (5th tool box from left), draw triangle ABC • using the midpoint tool (2nd tool box from left), plot the midpoint of segment AB, segment BC and segment CA • using the segment tool (3rd tool box from the left), draw the medians of triangle ABC • using the intersect tool (2nd tool box from left), create point G at the intersection of the medians • locate the transformation tool box (4th from right) • rotate triangle DEF 180 degrees about point G to create triangle D'E'F' • dilate triangle D'E'F', center of dilation G, scale 2 to create D"E"F" • in "options", select "labeling" and turn on "all new objects" • draw segment FG, segment GF' and segment F'F" to create j, k and l • using object properties, recolor each segment
1. Compare the lengths of segments j, k and l. What do you notice? 2. Using the move tool (left tool box), drag A. Does the relationship between the segments change? 3. Why does FG = GF'? 4. Why is GF" = 2(GF')? 5. What is the ratio between FG and GF"? 6. Does this ratio hold true for the segments of the other medians? 7. Rename point G "centroid". 8. Write a sentence containing something you discovered about the centroid in this activity.