determine vector of position of C if vector of position of A,B in triangle ABC are given. vec pA=4i+7j vecpB=2i-j vec pG=4i+4j g is centroid point

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should remember how you may find the coordinates of the centroid of a triangle ABC such that:

`x_G = (x_A + x_B + x_C)/3`

`y_G = (y_A + y_B + y_C)/3`

You may find the coordinates of vertices A and B and centroid G, using the give position vectors such that:

`bar p_A = 4bari + 7bar j => A(4,7)`

`bar p_B = 2bar i - bar j => B(2,-1)`

`bar p_G = 4bar i + 4bar j => G(4,4)`

You need to substitute the coordinates of A,B,G in equations of `x_G`  and `y_G`  such that:

`4= (4 +2 + x_C)/3 => 12 = 6 + x_C => x_C = 6`  `4= (7- 1+ y_C)/3 => 12 = 6 + y_C => y_C = 6`

Hence, evaluating the position vector of the vertex C yields `bar p_C = 6bar i + 6bar j` .

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