Question

please help!! using systems of linear equations...

the vertices of a triangle located at (-1, -1), (1, 3) and (4, 2). show that the medians of the triangle intersect at one point.

Answer 1

i think this takes a lot of work. we need to find the three medians
and therefore we need to find 3 midpoints as well as the equation for three lines
we can do it if you like, i do not see a snappy way to do this

Answer 2

actually now that i think about it, it is always true that the medians intersect at a single point. teh question probably is asking for you to find that point

Answer 3

I assume they want you to find the equations for each median, set up a system of equations, and show that there is exactly one solution (point of intersection)
the first step is to find the median points. Do you know how to do that?

Answer 4

nope... it's been 2 years since my last geometry class. :( sorry :( i forgot!!

Answer 5

can you plot the points (sketch it)?

Answer 6

http://en.wikipedia.org/wiki/Centroid#Of_triangle_and_tetrahedron
There is a formula here you can use....

Answer 7

We can show that the midpoint of a line segment with endpoints (x1,y1) and (x2,y2)
is the average x value and average y value
midpt = ( (x1+x2)/2 , (y1+y2)/2 )

make up a quick graph, label the points, label the mid points (use the formula)
now list the two points that lie on each median.
Here is a picture of 1 median http://www.proofwiki.org/wiki/Definition:Median_(Geometry)