Question

In ∆ABC, OA=3i-5j, OB=-7i+4j and the position vector of centroid G is 2i+j. Find OC.

Answer 1

Make a sketch.
Since position vector like OA = 3i-5j
set A as the point (3,-5), we also have
OB = -7i+4j , placing B at (-7,4)
let D be the midpoint of AB,
D = (-2, -1/2) using the standard way to find midpoint.
Also we know the centroid G is at (2,1)
We also know that the centroid is located 1/3 of the distance of the median measured from D

Let OC be the position vector ai + bj, so that C is (a,b)

vector DG = 1/3 vector DC
<4,3/2> = 1/3 <a+2, b+1/2>

(1/3)(a+2) = 4
a+2=12
a=10

(1/3)(b+1/2) = 3/2
b+1/2 = 9/2
b = 4

so OC = 10i + 4j

check my arithmetic