SOLUTION: Write the equation of the perpendicular bisector of the line segment with endpoints (-4,1) and (4,-3)
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Question 1125712: Write the equation of the perpendicular bisector of the line segment with endpoints (-4,1) and (4,-3)
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Write the equation of the perpendicular bisector of the line segment with endpoints
(,) and (,)
first find the equation of the line containing the segment with endpoints at (,) and (,) :
use given points to find a slope:
use one point to find
...........(,)
equation is:
now, recall:
A bisector cuts a line segment into two congruent parts. A segment bisector is called a perpendicular bisector when the bisector intersects the segment at a right angle.
the perpendicular bisector passes through the midpoint
so, first find the coordinates of the midpoint:
(,)
(,)
since bisector perpendicular to line segment, it is also perpendicular to line
and perpendicular lines have slopes negative reciprocal to each other
so, the perpendicular bisector will have a slope
....use midpoint (,) to find
->the equation of the perpendicular bisector
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