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

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

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:
<--><--> .
RELATED QUESTIONS
Can you please help me with this question: The altitudes of a triangle are concurrent (answered by jim_thompson5910)

A triangle is formed by the vertices A(1, 2), B(-5, -3), and C(1,-4) a.) Classify this (answered by MathLover1)

please help me! i dont know how to do this... find coordinates of for the centroid... (answered by Fombitz)

Prove that the triangle ABC whose vertices are A(2,-1), B(2,1) and C(-1,1) is a... (answered by Alan3354)

Find the coordinates of the centroid, orthocenter, and circumcenter of a triangle with... (answered by solver91311,richard1234)

Please help me solve this equation Find the area of a triangle whose vertices are (3,4),... (answered by Alan3354,ikleyn)

Triangle ABC has vertices A(-2, -3), B(2, 5), and C(6, -7). Find the circumcentre and the (answered by Edwin McCravy)

1.) Find the equation of the locus of a point moving such that its distance from the... (answered by josgarithmetic)

prove the following parallelograms is not rectangle? C(-9,4) D(-4,8) E(2,6)F (-3,2) ?... (answered by rothauserc)