If the vertices of a triangle are A(5, -1), B(-3, 1), and C(1, 5), what are the lengths of its medians? (Hint: Review the definition of a median of a triangle and the distance formula.)
The median is the line that bisects one side of the triangle. Thus a triangle has 3 medians. The midpoint of AB bisecting C The midpoint of BC bisecting A The midpoint of AC bisecting B Calculate the various midpoints. I will do one example for u. The midpoint of AB. Given A (5,-1) and B (-3,1) Midpoint of AB= ( (5+(-3))/2 , (-1+1)/2) = (1 , 0) This median will be joined by 2 points. The point (1,0) and point C. Calculate the length. Given C (1,5) Length = sqrt( (1-1)^2 + (5-0)^2 ) = sqrt( 5^2) = 5. Do the same for the other 2 medians.
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