Q. 194.5( 11 Votes )

# Find the length of medians of the triangle whose vertices are (1, –1), (0, 4) and (–5, 3).

We have the vertices of ∆ABC, A (1, –1), B (0, 4) and C (–5, 3).

Let D, E and F be the mid points of the sides BC, CA and AB respectively.

Using the mid–point formula,

Coordinates of D are

Coordinates of E are = (–2, 1)

Coordinates of F are

Using distance formula,

Length of median AD =

=

=

=

=

=

Length of median BE =

=

=

=

Length of median CF =

=

=

=

=

=

The lengths of medians of the triangle whose vertices are (1, –1), (0, 4) and (–5, 3) are and √13.

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