If A ( - 1, 6), B( - 3, - 9) and C(5, - 8) are the vertices of a ΔABC, find the equations of its medians.
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