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

Answer 1

Answer:

Equation of the line  that passes through the midpoint and is perpendicular to PQ is   2 x - y +1 = 0

Step-by-step explanation:

Step(i):-

Given points are P( -4 ,3 ) and Q ( 4,-1)

Mid -point of PQ

                     =      $(\frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2} )$

                    =       $(\frac{-4+4}{2} , \frac{3-1}{2} ) = ( 0 , 1 )$

Step(ii):-

Slope of PQ

             $m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } = \frac{-1-3}{4+4} = \frac{-4}{8} = \frac{-1}{2}$

The slope of the line is Perpendicular to PQ

           $m_{2} = \frac{-1}{m_{1} } = \frac{-1}{\frac{-1}{2} } = 2$

Equation of the line  that passes through the midpoint and is perpendicular to PQ

      $y - y_{1} = m ( x - x_{1} )$

          $y - 1 = 2 ( x - 0 )$

         2 x - y +1 = 0

Final answer:-

Equation of the line  that passes through the midpoint and is perpendicular to PQ

 2 x - y +1 = 0