Respuesta :
Equation of the line that passes through the midpoint and is perpendicular to PQ is 2x - y +1 = 0.
One way to describe a perpendicular bisector is as a line segment that cuts through another line segment at a 90 degree angle. Simply said, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle. Measuring a line segment that needs to be bisected will help you discover a perpendicular bisector.
The midway of the measured length can then be determined by dividing it by two. From this center, extend a line at a 90-degree angle. All you need to do to determine the perpendicular bisector of two points is to discover their midpoint and negative reciprocal, then enter these results into the slope-intercept form of the equation for a line.
Here points are P( -4 ,3 ) and Q ( 4,-1)
Mid -point of PQ :
[tex]=(\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )\\\\=(\frac{-4+4}{2} ,\frac{3-1}{2} )\\\\=(0,1)\\[/tex]
Slope of PQ:
[tex]m = \frac{y_{2}{-y_{1} } }{x_{2}{-x_{1} }} \\\\m =\frac{-1-3}{4+4}\\\\ m= \frac{-4}{8} \\\\m = \frac{-1}{2}[/tex]
The slope of the line is Perpendicular to PQ
so, slope 2= -1/m
slope 2 = -1/(-1/2)
slope 2 = 2
Equation of the line that passes through the midpoint and is perpendicular to PQ
[tex]y-y_{1} =m(x-x_{1}) \\y-1 =2(x-0}) \\\\y-1=2x\\[/tex]
2x - y +1 = 0.
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Correct Question:
Find the midpoint of PQ with endpoints P (-4, 3) and Q (4,-1) . Then write an equation of the line that passes through the midpoint and is perpendicular to PQ. This line is called the perpendicular bisector.
