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the vertex of triangle ABC are A(1 ,1 ,0) , B(1,2,1) and C(-2,2,-1) . find the equations of the medians through A and B use the equation so obtained to find the coordinates of the centroid

Posted by Pari Garg 1 year, 1 month ago

CBSE > Class 12 > Mathematics

1 answers

Manav Sharma 1 year, 1 month ago

To find the equations of the medians through points A and B, we first find the midpoints of the sides opposite to these vertices: 1. Midpoint of BC (opposite to A):

$(-0.5, 2, 0)$ 2. Midpoint of AC (opposite to B):

$(-0.5, 1.5, -0.5)$ Now, let's find the equations of the medians: ### Median through A: Equation:

$x + 1.5y - 2.5 = 0$ ### Median through B: Equation:

$2x + 3y - 2z - 4 = 0$ Now, let's solve these equations simultaneously to find the centroid's coordinates. By solving the equations of the medians simultaneously, we find the centroid's coordinates as (1.5, 5/4, 11/8).

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