SOLUTION: please help me solve this question The vertices of a triangle are (1,a)(2,b)(c square,-3):- (1) Prove that its centroid cannot lie on the Y

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Question 1011927: please help me solve this question
The vertices of a triangle are (1,a)(2,b)(c square,-3):-
(1) Prove that its centroid cannot lie on the Y - axis.
(2) Find the condition that the centroid may lie on the X - axis
Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!
(1) The centroid of a convex polygon is inside the polygon.
Since The x-coordinates of A, B, and C are all positive number,
so will be the x-coordinate of the centroid,
meaning that it will lie to the right of the y-axis.
Another way;
The x-coordinate of the centroid is the average of the x-coordinates of the vertices,
so it is ,
so the centroid lies on the line or to its right,
at a distance of at least to the right of the y-axis.

(2) The y-coordinate of the centroid is the average of the y-coordinates of the vertices,
so it is .
For the centroid to be on the x-axis, that y-coordinate must be zero:
<--><--> .

SOLUTION: please help me solve this question The vertices of a triangle are (1,a)(2,b)(c square,-3):- (1) Prove that its centroid cannot lie on the Y - axis. (2) Find the condition that