SOLUTION: The line segment joining a vertex of a triangle and the midpoint of the opposite side is called median of the triangle, the vertices of the triangle are A (4,-4), B (10,4) & C (2,6

Algebra ->  Length-and-distance -> SOLUTION: The line segment joining a vertex of a triangle and the midpoint of the opposite side is called median of the triangle, the vertices of the triangle are A (4,-4), B (10,4) & C (2,6      Log On


   

Question 1004794: The line segment joining a vertex of a triangle and the midpoint of the opposite side is called median of the triangle, the vertices of the triangle are A (4,-4), B (10,4) & C (2,6). Find the point on each median that is two-thirds of the distance from the vertex to the midpoint of the opposite side
Answer by Boreal(15235) About Me  (Show Source):
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Midpoints of each side is the average of the x values and y values of each end.
The midpoints are
(7,0),(6,5),(3,1)
The midpoint of the triangle is 2/3s the length of the median.
Find one vertex, and go 2/3s the way to the midpoint of the opposite side. Directions matter. Start at the point, and take 2/3s the x value and 2/3s the y-value.
The easiest one is 2/3s from (2,6) to (7,0)
The x-valueis 2/3s from 2 to 7. The distance is 5, and 2/3 of that is 10/3, or 3 1/3. So the x-value is 5 1/3 or 16/3. The y-value is 2/3 s from 6 to 0, or 2/3 of 6=4. The y-value is 2.
The midpoint is (16/3,2).
This will work for the other two points to the opposite side midpoint.