SOLUTION: im thinking of getting a tutor...however right now im really stuck on this question.Please help a.s.a.p A triangle has verticies A(0,4) B (-2,-2) C (6,2). Find the Centroid alg

Question 105898: im thinking of getting a tutor...however right now im really stuck on this question.Please help a.s.a.p
A triangle has verticies A(0,4) B (-2,-2) C (6,2).
Find the Centroid algebraically
thanks sooooooooooooooo much to who ever helps me.. I'm brutal with math ;)
Answer by HyperBrain(694) (Show Source): You can put this solution on YOUR website!
The centroid of a triangle is located at the intersection of the medians. A median is a line that originate from a corner of a triangle bisecting the opposite side.

Since you gave three points, it is a triangle and three unknown lines pass through these points.
First, let's find the line passing through A(0,4), and B (-2,-2).

Let m=slope

Now, let's find the slope-intercept form.
b is the y-intercept.
Let's use A (0,4) for x=0 and y=4.

Thus the equation of line1 is
Now, let's find the equation of the line passing through B (-2,-2) andf C (6,2).

Let's use B(-2,-2)

Thus the equation of the line is

let's find the equation of the line passing through A(0,4) and C(6,2)

Let'd use A (0,4)

threfore, the equation of the line is

If we graph this three lines,

They form the triangle

Now, we should find the equations of the 3 medians.

the 1st median passes through A(0,4) and the midpoint of B and C
Let D=the midpoint of B and C

Thus,
D=(2,0)
Now let's calculate the equation of the 1st median.

Let's use A(0,4)

Thus, the equation of the 1st median is

The 2nd median passes through B(-2,-2) and the midpoint of A and C.
Let E=the midpoint of A and C

Thus,
E=(3,3)
Calculate for the equation of the 2nd median.

Use E(3,3)

Thus, the equation of the second median is

The last median passes through C and the midpoint of A and B.
Let F=the midpoint of A and B

Thus,
F=(-1,1)
Solve for the equation of the last median.

Use F(-1,1)

Thus, the equation is

Locating the centroid,

It is located at (,)

Boy, that's challenging can I have my prize?

Power up,
HyperBrain!
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