Here given vertices are A (0,-1), B (2, 1) and C (0, 3) and let midpoints of BC, CA and AB be D,E and F respectively.
By midpoint formula.
x = \(\frac{x_1+x_2}2\), y = \(\frac{y_1+y_2}2\)
For midpoint D of side BC,
x = \(\frac{2+0}2\), y = \(\frac{1+3}2\)
x = \(\frac{2}2\), y = \(\frac{4}2\)
∴midpoint of side BC is D(1, 2)
For midpoint E of side AB,
x = \(\frac{0+0}2\), y = \(\frac{-1+3}2\)
x = \(\frac{0}2\), y = \(\frac{2}2\)
∴midpoint of side AB is E(0, 1)
For midpoint F of side CA
x = \(\frac{2+0}2\), y = \(\frac{1-1}2\)
x = \(\frac{2}2\), y = \(\frac{0}2\)
∴midpoint of side CA is F(1, 0)
By distance formula,
XY = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
For median AD,
AD = \(\sqrt{(1-0)^2+(2-(-1))^2}\)
= \(\sqrt{1+9}\)
= \(\sqrt{10}\) units
For median BE,
BE = \(\sqrt{(0-2)^2+(1-1)^2}\)
= \(\sqrt{4}\)
= 2 units
For median CF,
CF = \(\sqrt{(1-0)^2+(0-3)^2}\)
= \(\sqrt{1+9}\)
= \(\sqrt{10}\) units
