Question 30467
First of all, let's see what should the form of the segment AB be. We know that the line x = 2 is perpendicular to AB. Since x = 2 is a vertical line, then the segment AB must be horizontal (ie, parallel to the x-axis)

Given that the segment AB is horizontal, and that the point A is at (-4, 1), then the y-coordinate of B must be 1, just as the y-coordinate of A. If this weren't so, then the segment would not be horizontal. So the coordinates of point B must be (X, 1) (we still need to find X).

Now, we know that x=2 is not only perpendicular to AB, but it's also its bisector, meaning that it 'splits' the segment AB into two equally sized segments. We know that one of the extremes of the segment (the point A) is at X=-4, and that its middle point is at X=2. Therefore, it's clear that the other extreme of the segment must be at X=8 (there are 6 units from -4 to 2, and 6 units from 2 to 8; so 2 is the middle point of -4 and 8).

So we conclude that point B is located at (8, 1).

I hope this helps!

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