SOLUTION: 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

Algebra ->  Surface-area -> SOLUTION: 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      Log On


   

Question 1185395: 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) About Me  (Show Source):
You can put this solution on YOUR website!


A(7,-4)
B(a,b)
C(c,d)

The coordinates of the centroid are the averages of the coordinates of the three vertices:

%287%2Ba%2Bc%29%2F3=1
7%2Ba%2Bc=3
a%2Bc=-4

%28-4%2Bb%2Bd%29%2F3=2
-4%2Bb%2Bd=6
b%2Bd=10

The coordinates of the midpoint (m,n) of BC are the averages of the coordinates of B and C:

m=%28a%2Bc%29%2F2+=+-4%2F2+=+-2
n=%28b%2Bd%29%2F2+=+10%2F2+=+5

ANSWER: the midpoint of BC is (m,n)=(-2,5)