Question 627731: The centroid of triangle ABC is at point (6,0), the orthocentre at point(7,14/3),and the circumcentre at point (53/9, -7/3). They are collinear. what is the equation of the line passing through these points and how do i get there because my teacher has not taught us this but expects us to know.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Your three points are not collinear.
However, you only need two points to define a line. In general, use the two-point form of an equation of a line:
(x\ -\ x_1) )
where ) and ) are the coordinates of the given points.
Just plug in the numbers, do the arithmetic, and simplify.
By the way, here is how I know that your three points are not collinear:
If three points lie on the same line, then the slope of the segment between any of pair of them must be equal. Use the slope formula:
where and are the coordinates of the given points.
to calculate the slope between each of the three pairs of points (centroid/orthorcenter, orthocenter/circumcenter, and circumcenter/centroid), You will find that you get three different results, hence the three points are not collinear.
John
My calculator said it, I believe it, that settles it
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