Question 256075
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*[tex \LARGE x\ =\ 2] is a vertical line.  Therefore the line containing the segment AB must be a horizontal line.  All points in any horizontal line have identical *[tex \LARGE y] coordinates.  Therefore, since the *[tex \LARGE y]-coordinate of A(-4,1) is 1, the *[tex \LARGE y]-coordinate of point B must also be 1.


The *[tex \LARGE x]-coordinate of all points in any given vertical line are identical.  Therefore, the *[tex \LARGE x]-coordinate of all points on the line *[tex \LARGE x\ =\ 2] is 2.  That means that the midpoint of the segment AB must be (2,1).


The midpoint formula for *[tex \LARGE x] gives the *[tex \LARGE x]-coordinate of the midpoint given the *[tex \LARGE x]-coordinates of the endpoints:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_m\ = \frac{x_A + x_B}{2}]


But here we know the *[tex \LARGE x]-coordinate of one of the endpoints and the *[tex \LARGE x]-coordinate of the midpoint.  So solve the formula for *[tex \LARGE x_B]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_B\ =\ 2x_m\ -\ x_A]


Substitute the known values and do the arithmetic.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_B\ =\ 2(2)\ -\ (-4)\ =\ 8]


Therefore B is the point (8, 1)


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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