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
