## 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

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

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