Question

Find the length of the medians of a triangle whose vertices are A(-1,3),B(1,-1)and C(5,1).

Answer 1

Answer:

median from A= 5 units

similarly we can find length of remaining 2 medians.

Explanation:

median O(x,y) = ((-1+1+5)/3, (3+-1+1)/3)

=(5/3, 1)

length of median =3/2 ( AO)

$= \frac{3}{2} \sqrt{( \frac{5}{3} - (- 1)) ^{2} + {(1 - 3)}^{2} }$

$\frac{3}{2} \sqrt{ { \frac{8}{3} }^{2} + {( - 2)}^{2} }$

$= \frac{3}{2} \sqrt{ \frac{64}{9} + 4 }$

$= \frac{3}{2} \sqrt{ \frac{100}{9} }$

$= \frac{3}{2} \times \frac{10}{3}$

= 5 units