How might you prove your observations in Question 2 using algebra and x and y-coordinates? Briefly outline an approach using what you know about a midpoint and the slope of a line.

I can use variables to represent the coordinates of the vertices for a general triangle, ∆ABC. Then I can calculate the midpoints of the sides in terms of those variables. Using the point-slope formula for the equation of a straight line, I can build the symbolic equations for the three medians, AE, BF, and CD. I can solve for the point of intersection for two of the medians, AE and BF, for example. Finally, I can prove the lines (i.e., medians) concurrent if the point I found also satisfies the equation of the line for CD.

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step-by-step explanation:

step-by-step explanation:

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