MHB Perpendicular Bisector: Understanding the Wording

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The discussion focuses on understanding the concept of a perpendicular bisector in geometry. It clarifies that the slope of a line through two points can be calculated, and for two perpendicular lines, their slopes multiply to -1. The midpoint between the points (1, 2) and (-5, -4) is determined to be (-2, 3). The next step involves finding the equation of the line that passes through this midpoint with a slope of -1. The conversation emphasizes the importance of both the midpoint and the negative reciprocal relationship of slopes in defining the perpendicular bisector.
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I know that when two lines are perpendicular their gradients multiply to -1 but I don't get the wording here.
Any suggestions?
 

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The line through (1, 2) and (-5, -4) has slope $\frac{-5- 1}{-4- 2}= \frac{-6}{6}= 1$ so any line perpendicular to that has slope -1. Further the perpendicular **bisector** goes through the point exactly half way between (1, 2) and (-5, 4) which is $\left(\frac{1+ (-5)}{2}, \frac{2+ 4}{2}\right)$$= \left(\frac{-4}{2},\frac{6}{3}\right)= (-2, 3)$.

What is the equation of the line through (-2, 3) with slope -1?
 
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