Q. 193.5( 6 Votes )

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Answer :

Construction: - Draw median from vertices A, B and C on lines BC,AC and AC respectively .Let the mid - points of lines BC,AC and AB be L,M and N respectively.

Now find the coordinate of L, M and N using mid - point theorem.







Now equation of medians AL, BM and CN using two point form


For median AL,





4(y - 6) = - 29(x + 1)


4y - 24 + 29x + 29 = 0


29x + y + 5 = 0


For median BM,





5y + 45 = 8x + 24


8x - 5y + 24 - 45 = 0


8x - 5y - 21 = 0


For median CN,





4(y + 8) = 13(x - 5)


4y + 32 = 13x - 65


13x - 4y - 65 - 32 = 0


13x - 4y - 97 = 0


So, the required line of equations for medians are for AL: 29x + y + 5 = 0


For BM: 8x - 5y - 21 = 0


For CN: 13x - 4y - 97 = 0


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