Find the lengths of the medians AD and BE of

Question:

Find the lengths of the medians $A D$ and $B E$ of $\Delta A B C$ whose vertices are $A(7,-3), B(5,3)$ and $C(3,-1)$.

 

Solution:

The given vertices are A(7, −3), B(5, 3) and C(3, −1).
Since D and E are the midpoints of BC and AC respectively, therefore

Coordinates of $D=\left(\frac{5+3}{2}, \frac{3-1}{2}\right)=(4,1)$

Coordinates of $E=\left(\frac{7+3}{2}, \frac{-3-1}{2}\right)=(5,-2)$

Now

$A D=\sqrt{(7-4)^{2}+(-3-1)^{2}}=\sqrt{9+16}=5$

$B E=\sqrt{(5-5)^{2}+(3+2)^{2}}=\sqrt{0+25}=5$

Hence, AD = BE = 5 units.

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