lengths of medians

Asked by abhishek agrawal | 11th Feb, 2014, 12:15: PM

Expert Answer:

Let A = (1, -1), B=(0,4), C=(-5,3)
Let AD be the median through A.
Median AD of the triangle will divide the side BC in two equal parts. So D is the midpoint of side BC.
The coordinates of D are given by

open parentheses fraction numerator 0 minus 5 over denominator 2 end fraction comma fraction numerator 4 plus 3 over denominator 2 end fraction close parentheses identical to open parentheses minus 2.5 comma space 3.5 close parentheses
Thus, using distance formula, length of median through A = Length of AD
 
equals square root of left parenthesis 1 plus 2.5 right parenthesis squared plus left parenthesis minus 1 minus 3.5 right parenthesis squared end root
 
equals square root of left parenthesis 3.5 right parenthesis squared plus left parenthesis minus 4.5 right parenthesis squared end root
equals square root of 12.25 plus 20.25 end root
 
equals square root of 32.5 end root units
Similarly, lengths of other two medians can be found.

Answered by  | 11th Feb, 2014, 04:45: PM

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