How to Find the Median of a Triangle?

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 M_a,M_b and M_c.

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 m_a = (1/2) √2c² + 2b² - a² m_b = (1/2) √2c² + 2a² - b² m_c = (1/2) √2a² + 2b² - c² m_a = (1/2)√2(8.062)² + 2(4.123)² - 4.242² = 6.042 m_b = (1/2)√2(8.062)² + 2(4.242)² - 4.123² = 6.103 m_c = (1/2)√2(4.242)² + 2(4.123)² - 8.062² = 1.118