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A perpendicular bisector usually means a line which 'cuts' a segment in half exactly, and is perpendicular to it. I say segment and not line, because a line extends to infinite in both directions and there is no concept of cutting something of infinite length in half.
You can bisect other things like angles using lines.
Thanks, that helped a lot !
Also, the gradient f a segment is the same as the gradient of a line which is parallel to it call this line \[l_1.\] Your perpendicular bisector which we are going to call \[l_2\] must be perpendicular to \[l_1\] and so it will be perpendicular to the segment that you want to bisect.