Respuesta :
The Equation of perpendicular bisector line l is found to be [tex]y = 2x+ 11[/tex]
Given Line XY is formed by points X(-9, -7) and Y(-3,5) therefore, it passes through these two respective points.
Let the slope of this line be n
The Slope of line passing through X and Y points is given by
n = [tex](y_{2} - y_{1} )/(x_{2} -x_{1} )[/tex]
⇒ n = {5 - (-7) }/ {(-3) - |(-9)}
⇒ n = 12/6
⇒ n = 2 (equation 1 )
Given that line l is perpendicular bisector of XY
Let the slope of l = m
We know that the product of the slopes of any two perpendicular lines is -1
Therefore, n x m = -1
⇒ m = -1 \ n
putting the value of n from the above equation 1 we get
⇒ m = - 1/2
Additionally, because l is the perpendicular bisector hence it goes through the mid point of the line XY
Mid point of two lines = [tex](x_{2} + x_{1} )/2[/tex] and [tex](y_{2} + y_{1} )/2[/tex]
Mid point of XY = [tex]\frac{-9 + (-3)}{2}[/tex] and [tex]\frac{-7 + (5)}{2}[/tex]
= (-6, -1)
The equation of perpendicular bisector l is given my the following formula:
[tex]y = nx + c[/tex]
here we have n = slope of line
we have n = 2 from equation 1
∴ y = 2x + c (equation 2)
Also equation (2) is satisfied by the point (-6,-1)
Hence we can express it as:
-1 = 2(-6) + c
⇒ c = 11
Therefore the required equation of perpendicular bisector l is
[tex]y = 2x + 11[/tex]
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