Answer:
[tex]y=1.6x+2.1[/tex]
Step-by-step explanation:
we know that
The right bisector of the line segment JK is a perpendicular line to the segment JK that pass through the midpoint of segment JK
step 1
Find the midpoint JK
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
[tex]J(-5,3),K(3,-2)[/tex]
substitute the values
[tex]M(\frac{-5+3}{2},\frac{3-2}{2})[/tex]
[tex]M(\frac{-2}{2},\frac{1}{2})[/tex]
[tex]M(-1,\frac{1}{2})[/tex]
step 2
Find the slope JK
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]J(-5,3),K(3,-2)[/tex]
substitute
[tex]m=\frac{-2-3}{3+5}[/tex]
[tex]m=\frac{-5}{8}[/tex]
[tex]m=-\frac{5}{8}[/tex]
step 3
Find the slope of the line perpendicular to the segment JK
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=-\frac{5}{8}[/tex] ----> slope of segment JK
Find m_2
substitute
[tex](-\frac{5}{8})*m_2=-1[/tex]
[tex]m_2=\frac{8}{5}[/tex]
step 4
Find the equation for the right bisector of the line segment JK
The equation in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{8}{5}[/tex]
[tex]point\ M(-1,\frac{1}{2})[/tex]
substitute
[tex]y-\frac{1}{2}=\frac{8}{5}(x+1)[/tex]
Convert to slope intercept form
isolate the variable y
[tex]y-\frac{1}{2}=\frac{8}{5}x+\frac{8}{5}[/tex]
[tex]y=\frac{8}{5}x+\frac{8}{5}+\frac{1}{2}[/tex]
[tex]y=\frac{8}{5}x+\frac{21}{10}[/tex]
[tex]y=1.6x+2.1[/tex]
