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Question 1091607: Point M is the midpoint of AB. The coordinates of point A are (-8, 3) and the coordinates of M are (-2, 1). What are the coordinates of point B?
Thank you! I don't understand too much..):
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! midpoint between (x1, y1) and (x2, y2) is the average of the x s and the average of the y s
Here, one has the midpoint, so work backward to get the other point.
the midpoint for the x values is -2. One value is -8, so (-8 +x2)/2=-2, the average of the two points is -2
-2=(-8 +x2)/2
multiply by 2 and -4=x^2-8, and x2=4.
Do the same thing with y
You can think of it this way. The middle is y=1, and one side is 3. That is two away from the middle, so the other side has to be 2 on the other side of the middle, or -1
The coordinates of B are (4, -1).
Check by adding the A and B points and taking the average: -8+4 divided by 2 is -4/2=-2.
-1+3/2 is 2/2=1
Answer by ikleyn(52785)  (Show Source):
You can put this solution on YOUR website! .
X-coordinate of the point B is the sum Bx = Mx + (Mx - Ax) = -2 + (-2 - (-8)) = -2 + (-2 + 8) = -2 + 6 = 4.
y-coordinate of the point B is the sum By = My + (My - Ay) = 1 + (1 - 3) = 1 - 2 = -1.
Answer. B = (4,-1).
HINT. To make it clear, plot these points in a graph paper.
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