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How do i find the length of a triangles median.

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user3517441 | eNotes Newbie

Posted February 22, 2013 at 3:49 AM via web

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How do i find the length of a triangles median.

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lfryerda | High School Teacher | (Level 2) Educator

Posted February 24, 2013 at 2:02 PM (Answer #1)

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A median is the line segment that goes from a vertex to the middle of the opposite side.

It is simplest to show how to find the length of the median using an example.  Consider the triangle with points A(3,5), B(1,2) and C(5,4). These numbers were just made up, and are quite arbitrary.  

The median from the vertex A goes to the midpoint of the line segment BC.  The midpoint of BC is found using the midpoint formula:

`M({1+5}/2,{2+4}/2)=M(3,3) `

To find the length of the line segment, now use the distance formula from A to M.

`d=sqrt{(3-3)^2+(5-3)^2}`

`=sqrt{0^2+2^2}`

`=sqrt4`

`=2`

so the length is 2.

To find the length of a median of a triangle, use the distance formula from the vertex of the triangle to the midpoint of the opposite side.

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