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Question
Two vertices of a triangle are (1, 4) and (3, 1). If the centroid of the triangle is the origin, find the third vertex.
Solution
Given the centroid of Δ ABC is at origin , i.e. G (0 , 0).
Let the coordinates of third vertex be (x , y).
Coordinates of G are ,
G (0 , 0) = G `((1 + 3 + "x")/3 , (4 + 1 + "y")/3)`
O = `(4 + "x")/2` , O = `(5 + "y")/2`
x = - 4 , y = -5
Coordinates of third vertex are (-4 , -5)
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