plz help...i have a big math test 2morrow that i need 2 pass

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i need help on the questions:

What are the coordinates of the centroid of a triangle whose vertices are A(3,1), B(7,3), & C(5,7)?

A:(5,11/3) B:(5,16/3) C:(5,2) D:(6,8/3) E(6,11/3)


can sum1 please explain this problem 2 me, how you would solve it but not by just simply drawing & finding the point, since we're not allowed 2 do that
 
First step: If you're not sure, find the definition of "centroid" and how the centroid relates to the vertices.

If you've got that, then please reply with the definition and relationship you're using, along with any further progress you've made.

Thank you.

Eliz.
 
im using the midpoint formula & then subtracting the empty distance on the grid from the triangle
 
Median: The line drawn from a triangle's vertex to the midpoint of the opposide side.

So you're needing to find where the medians intersect. A good place to start would be the Midpoint Formula, finding the mipoints of the sides opposite the various vertices. I'm afraid I have no idea what you mean by "subtracting the empty distance on the grid", however.

Since you know that all three medians cross at the same place, and since you know that you can find this mutual intersection point by finding where any two of the lines cross, just find two of the lines.

Pick two points and their opposite sides. The process for each point-opposite-side set will be the same. For instance, if you pick point A, then you would first find the midpoint of side BC. Then find the slope of the line between A and this midpoint. Then, with A and the slope, find the line equation, "y = mx + b". Do the same for one of the other points. Then set the two line equations equal, and solve for "x". Plug this into either of the line equations to find "y".

The point (x, y) is the solution they're looking for.

There may be another method, but since your book apparently hasn't provided anything on the topic, this would be how I would proceed.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.
 
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