Question

Find the lengths of the medians $RS$ and $PT$ of a triangle $PQR$ whose vertices are $P(6,-2),Q(6,3)$ and $R(3,1)$

Answer 1

Point S and T are mid points of PQ and QR respectively.

Then coordinate of $S=\left[6,\frac{1}{2}\right]$

and coordinate of $T=\left[\frac{9}{2},2\right]$

Length of median $RS=\sqrt{{\left(3\right)}^2+{\left(\frac{1}{2}\right)}^2}=\sqrt{9+\frac{1}{4}}$

$RS=\sqrt{\frac{37}{4}}=\frac{\sqrt{37}}{2}unit$

Length of median $PT=\sqrt{{\left(\frac{3}{2}\right)}^2+{\left(-4\right)}^2}=\sqrt{\frac{9}{4}+16}$

$PT=\frac{\sqrt{73}}{2}$