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 p

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

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Sigridomena 1 year 2021-07-29T01:05:32+00:00 1 Answers 11 views 0

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    2021-07-29T01:07:13+00:00

    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

                         =      [tex](\frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2} )[/tex]

                        =       [tex](\frac{-4+4}{2} , \frac{3-1}{2} ) = ( 0 , 1 )[/tex]

    Step(ii):

    Slope of PQ

                 [tex]m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } = \frac{-1-3}{4+4} = \frac{-4}{8} = \frac{-1}{2}[/tex]

    The slope of the line is Perpendicular to PQ

               [tex]m_{2} = \frac{-1}{m_{1} } = \frac{-1}{\frac{-1}{2} } = 2[/tex]

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

          [tex]y – y_{1} = m ( x – x_{1} )[/tex]

              [tex]y – 1 = 2 ( x – 0 )[/tex]

             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

               

               

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )