If point C is the midpoint of AB, what is the coordinate of point B?

(3, 1)
(4, 2)
(4, 4)
(3, 0)

Question

If point C is the midpoint of AB, what is the coordinate of point B? 

(3, 1) 
(4, 2) 
(4, 4) 
(3, 0)

anonymous · Answer

Here is the picture

e.mccormick · Answer

Well, if it is the midpoint, then it is half way up and half way over.  So, you find the total change in x and y, then take half of that, and add it to the bottom point.  That is one way to do it.  Or you can add the points and halv that.

anonymous · Answer

Thank you both so much.

e.mccormick · Answer

Ah, this is going from the midpoint, I was talking about finding the idpoint.  My mistake.  So you woul double the up over in this case.

anonymous · Answer

Let B=(x,y)
Then   3 = (x+2)/2
0 = (y-4)/2

anonymous · Answer

Ok, so  4,4

e.mccormick · Answer

Yes. Sorry bout the mistake.  Hope you get the idea they are related.  Lets you answer any of them easily.

anonymous · Answer

Yes thank you

amistre64 · Answer

my idea is:  since midpoint is average of the other 2 points ..$$\frac{A+B}{2}=C$$
$$B=2C-A$$

anonymous · Answer

Thank you

amistre64 · Answer

2C = 2(3,0) =   (6  , 0)
-A = -(2, -4) = (-2, 4)
                     ----------
        2C-A =     ( 4 , 4)

anonymous · Answer

Thank you, makes sense now