The midpoint of start overline, AB, end overline AB is M, left bracket, minus, 1, comma, 5, right bracketM(−1,5). If the coordinates of AA are left bracket, minus, 7, comma, 7, right bracket(−7,7), what are the coordinates of BB?
Question
The midpoint of start overline, AB, end overline AB is M, left bracket, minus, 1, comma, 5, right bracketM(−1,5). If the coordinates of AA are left bracket, minus, 7, comma, 7, right bracket(−7,7), 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.
Let's denote the coordinates of B as (x2, y2).
We can set up the following equations using the midpoint formula:
-1 = (-7 + x2)/2 and 5 = (7 + y2)/2
Solving these equations for x2 and y2 will give us the coordinates of B.
For the x-coordinate:
-1 = (-7 + x2)/2 -2 = -7 + x2 x2 = -2 + 7 x2 = 5
For the y-coordinate:
5 = (7 + y2)/2 10 = 7 + y2 y2 = 10 - 7 y2 = 3
So, the coordinates of B are (5, 3).
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