Here given vertices of triangle are A (-1, 3), B (1, -1) and C (5, 1).
Let D, E and F be the midpoints of the sides BC, CA and AB respectively.
We need to find length of median passing through A, ie distance between AD.
Let point D ≡ (x, y)
By midpoint formula,
x = \(\frac{x_1 + x_2}2\), y = \(\frac{y_1 + y_2}2\)
For midpoint D of side BC,
x = \(\frac{1 + 5}2\), y = \(\frac{-1 + 1}2\)
∴ x = \(\frac{6}2\), y = \(\frac{0}2\)
∴D(x , y) ≡ (3, 0 )
Now,
by distance formula,
XY = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
For AD,
AD = \(\sqrt{(3 - (-1))^2 + (0 - 3)^2}\)
∴ AD = \(\sqrt{16 + 9}\)
AD = \(\sqrt{25}\)
∴AD = 5 units
Hence,
the length of the median through A is 5 units
