The midpoint of start overline, AB, end overline AB is M, left bracket, minus, 3, comma, 1, right bracketM(−3,1). If the coordinates of AA are left bracket, 1, comma, 6, right bracket(1,6), what are the coordinates of BB?
Question
The midpoint of start overline, AB, end overline AB is M, left bracket, minus, 3, comma, 1, right bracketM(−3,1). If the coordinates of AA are left bracket, 1, comma, 6, right bracket(1,6), what are the coordinates of BB?
Solution
The midpoint formula is given by M = [(x1 + x2)/2 , (y1 + y2)/2]. Here, M is the midpoint, (x1, y1) are the coordinates of point A, and (x2, y2) are the coordinates of point B.
We know that M = (-3, 1) and A = (1, 6). We can set up the following equations to solve for the coordinates of B (x2, y2):
For the x-coordinate: -3 = (1 + x2)/2 Multiply both sides by 2 to get rid of the fraction: -6 = 1 + x2 Subtract 1 from both sides: -7 = x2
For the y-coordinate: 1 = (6 + y2)/2 Multiply both sides by 2: 2 = 6 + y2 Subtract 6 from both sides: -4 = y2
So, the coordinates of point B are (-7, -4).
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