Question

Find the lengths of the medians AD and BE of $∆ABC$ whose vertices are A(7, −3), B(5, 3) and C(3, −1). [CBSE 2014]

Answer 1

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
$$\begin{gathered} \mathrm{Coordinates}\mathrm{of}D=\left(\frac{5+3}{2},\frac{3-1}{2}\right)=\left(4,1\right) \\ \mathrm{Coordinates}\mathrm{of}E=\left(\frac{7+3}{2},\frac{-3-1}{2}\right)=\left(5,-2\right) \end{gathered}$$
Now
$$\begin{gathered} AD=\sqrt{{\left(7-4\right)}^2+{\left(-3-1\right)}^2}=\sqrt{9+16}=5 \\ BE=\sqrt{{\left(5-5\right)}^2+{\left(3+2\right)}^2}=\sqrt{0+25}=5 \end{gathered}$$
Hence, AD = BE = 5 units.