Investigating the Centroid using Transformations

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

Informació: Investigating the Centroid using Transformations