# How to Find the Median of a Triangle?

## Median of a Triangle - Definition, Formula and Example

##### Definition:

In a triangle, a median is a line joining a vertex with the mid-point of the opposite side. Every triangle have 3 medians. Their standard notated as Ma,Mb and Mc.

#### Formula:

ma = (1/2) √2c2 + 2b2 - a2 mb = (1/2) √2c2 + 2a2 - b2 mc = (1/2) √2a2 + 2b2 - c2 Where a,b,c - Length of triangle sides.
##### Example:

Given the points A( 1 , 5 ), B( 8 , 9 ) and C( 5 , 6 ), Find the medians of triangle.

##### Given:

A( 1 , 5 ) B( 8 , 9 ) C( 5 , 6 )

##### Solution:
###### Step 1:

Find triangle side lengths a,b,c using distance formula

d = √(x2 - x1)2 + (y2 - y1)2

Find triangle side a Length Between points B( 8 , 9 ) and C( 5 , 6 ) a = √(5 - 8)2 + (6 - 9)2 = 4.242

Find triangle side b Length Between points C( 5 , 6 ) and A( 1 , 5 ) b = √(1 - 5)2 + (5 - 6)2 = 4.123

Find triangle side c Length Between points A( 1 , 5 ) and B( 8 , 9 ) c = √(8 - 1)2 + (9 - 5)2 = 8.062

##### Step 2:

Subsuite a,b,c values in given formula ma = (1/2) √2c2 + 2b2 - a2 mb = (1/2) √2c2 + 2a2 - b2 mc = (1/2) √2a2 + 2b2 - c2 ma = (1/2)√2(8.062)2 + 2(4.123)2 - 4.2422 = 6.042 mb = (1/2)√2(8.062)2 + 2(4.242)2 - 4.1232 = 6.103 mc = (1/2)√2(4.242)2 + 2(4.123)2 - 8.0622 = 1.118