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Question 1173445: the midpoint of AB is M (3,-2) if the coordinates of A are (1,-3), what are the coordinates of B?
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
Using formal algebra....
The x and y coordinates of the midpoint are the averages of the x and y coordinates of the two endpoints.
A(1,-3)
M(3,-2)
B(m,n)
(m+1)/2 = 3 --> m+1 = 6 --> m = 5
(n-3)/2 = -2 --> n-3 = -4 --> n = -1
ANSWER: B(5,-1)
You should understand how that process gives you the answer; and you should know how to solve the problem by that method.
But if solving without formal algebra is allowed, an informal solution is much faster and easier:
From A(1,-3) to the midpoint M(3,-2) is 2 units to the right and 1 unit up; from the midpoint M(3,-2) to the other endpoint B is again 2 units to the right and 1 unit up:
B is (3+2,-2+1) = (5,-1).
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