SOLUTION: Two vertices of a triangle are (0,6) and (4,0), and the medians intersect at (0,2). Find the third vertex of the triangle.

Question 345491: Two vertices of a triangle are (0,6) and (4,0), and the medians intersect at (0,2). Find the third vertex of the triangle.
Found 2 solutions by Fombitz, ewatrrr:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
A:(,)
B:(,)
C:(,)
Assume that the final vertex is located at(,).
Then the median connecting (,) to the midpoint of , located at (,), has a slope,since it also goes through (,), of,

and a y-intercept of .
1.
.
.
.
The median connecting (,),(,), and the midpoint of has a slope of,

and a y-intercept of .

The midpoint of is (,) or (,).
It also satisfies the line,

2.
.
.
.
From eq. 1,

Substituting into eq. 2,

Then

The final vertex is located at (,)

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
Hi,
Recommend Sketching out the points given first:

The question states medians intersect at pt(0,2)
*Note: Medians go from a vertex to the midpoint of the opposing side
.
Sketch determines the midpoint of the opposing side of vertex (0,6) would be (0,0)
.
the third vextex would be (-4,0)
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