If A( 5,-1), B( -3,-2) and C(-1,8) are the vertices of triangle ABC, then find the length of median through A and the coordinates of the centroid
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Let AD be the median through the vertex A of△ABC. Then, D is the mid-point of BC. So, the coorinates of D are( 2−3−1 , 2−2+8 )i.e.,(−2,3).
∴AD= (5+2) 2 +(−1−3) 2
= 49+16
= 65 units
Let G be the centroid of △ABC. Then, G lies on median AD and divides it in the ratio 2:1. So, coordinates of G are( 2+12×−2+1×5 , 2+12×3+1×− )=( 3−4+5 , 36−1 )=( 31 , 35 )
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