The midpoint of start overline, AB, end overline AB is M, left bracket, minus, 2, comma, minus, 6, right bracketM(−2,−6). If the coordinates of AA are left bracket, minus, 3, comma, minus, 4, right bracket(−3,−4), what are the coordinates of BB?
Question
The midpoint of start overline, AB, end overline AB is M, left bracket, minus, 2, comma, minus, 6, right bracketM(−2,−6). If the coordinates of AA are left bracket, minus, 3, comma, minus, 4, right bracket(−3,−4), what are the coordinates of BB?
Solution
The midpoint formula is given by M = [(x1 + x2)/2 , (y1 + y2)/2].
Here, we know the coordinates of M and A, and we need to find the coordinates of B (x2, y2).
We can set up the following equations using the midpoint formula:
-2 = (-3 + x2)/2 and -6 = (-4 + y2)/2
Solving these equations for x2 and y2 will give us the coordinates of B.
For the x-coordinate:
-2 = (-3 + x2)/2 Multiply both sides by 2: -4 = -3 + x2 Add 3 to both sides: -1 = x2
For the y-coordinate:
-6 = (-4 + y2)/2 Multiply both sides by 2: -12 = -4 + y2 Add 4 to both sides: -8 = y2
So, the coordinates of B are (-1, -8).
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