Thread: Finding the Centroid of this triangle - stuck!

I have a triangle CDE

The coordinates for the vertices are C(-2,4) D(6,2) and E(-4,-2)

I have found the mid points of CD (2,3) and CE (-3,1)

I have also found the equation of the median for FE: Y = 5x/6 + 4/3 and GD: Y = x/9 + 4/3

The problem is that I can't solve the system of equations:

1. y= 5x/6 + 4/3
2. y= x/9 + 4/3

I've tried substituting 1. in to 2. but I end up with:
x/9 + 4/3 = 5x/6 + 4/3

Does anyone know where I've gone wrong?

If you want to solve the sytem, substitution is a good solution, you'll get:




Get a common denominator and a fraction becomes zero if the numerator because zero ...

Notice if the three vertices of a triangle ABC are then the coordinates of the centroid of the triangle is:

You should know also that:

In triangle , with \text{A}=(x_1,y_1), \text{B}=(x_2,y_2), \text{C}=(x_3,y_3).

The centroid is given by:

.


Try to prove the above using the same arguments that you use with your problem(just replace the coordinates)


Edit:

Sorry @Siron, didn't see your edited post.

Thank you for the replies. I came back here with the problem solved however.

I realized that I could multiply each number by 18 since 18 is a common denominator of \frac{x}{9}+\frac{4}{3}=\frac{5x}{6}+\frac{4}{3}

When I did this, I ended up with the correct Centroid. I proved it by making a model in Geometers Sketch Pad and I ended up with the same centroid as the model.

Thanks!

You're welcome!

@ Also sprach Zarathrusta:
No problem