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The equation of the perpendicular bisector of the segment with endpoints y(10,−7) and z(−4,1) is (y+3)=[tex]\frac{-7}{4}[/tex](x-3).
Given that a line segment has endpoints y(10,-7) and z(-4,1) and asked to find the perpendicular bisector.
The equation of the perpendicular bisector will pass through the midpoint of the line segment having endpoints y(10-7) and z(-4,1)
The midpoint of the line segment having endpoints y(10-7) and z(-4,1) is (3,-3)
As the midpoint formula is ([tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex]) for a line segment having endpoints (x1,y1) and (x2,y2).
The slope of the perpendicular bisector will be the [tex]\frac{-1}{slope of given line}[/tex]
The slope of given line=[tex]\frac{-7-1}{-4-10}[/tex]=[tex]\frac{4}{7}[/tex]
The slope of the perpendicular bisector=[tex]\frac{-7}{4}[/tex]
The equation of perpendicular bisector=(y+3)=[tex]\frac{-7}{4}[/tex](x-3).
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