Question 1185390: 3. The coordinates of vertex A of the triangle ABC are (7, -4). If the coordinates of the centroid of the triangle are (1, 2), find the coordinates of the midpoint of the side BC.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Let D be the midpoint of side BC.
The three medians of any triangle meet at the centroid.
The point of intersection of the three medians divides each median into two parts whose lengths are in the ratio 2 to 1.
To state that differently, on each median, the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint of the opposite side.
Using that, the problem is most easily solved informally, using logical reasoning and simple arithmetic.
Vertex A is at (7,-4); the centroid is at (1,2).
From the vertex to the centroid is a distance -6 in the x direction and +6 in the y direction, so from the centroid to midpoint D of side BC is half those distances: -3 in the x direction and +3 in the y direction.
-3 in the x direction and +3 in the y direction from the centroid (1,2) puts us at (-2,5).
ANSWER: (-2,5)
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