# vectors of A,B,G: RA=4i+7j, RB=2i-j,RG=4i+4j what is vector of C if G centroid of triangle ABC?

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to remember that you may write the position vector of a point if you know the  coordinates of point.

You should come up with the following coordinates for the point C such that: C(a,b), hence the vector of position is `bar r_C = a bar i + b bar j.`

You need to remember that the vector of position of centroid of triangle ABC is `bar r_G = (1/3)(bar r_A + bar r_B+ bar r_C),`  hence, plugging the given vectors in relation yields:

`4bar i+4bar j = (1/3)(4bar i+7bar j + 2bar i - bar j + a bar i + b bar j)`

`4bar i+4bar j = (1/3)(6bar i+6bar j + a bar i + b bar j)`

`4bar i+4bar j = (1/3)((6+a)bar i + (6+b)bar j)`

Equating the coefficients of `bar i`  and `bar j`  yields:

`(6 + a)/3 = 4 =gt a + 6= 12 =gt a = 6`

`(6 + b)/3 = 4 =gtb + 6= 12 =gtb = 6`

Hence, the position vector of the vertex C is `bar r_C = 6 bar i + 6 bar j.`