Answer:
y = - 6x + 7.5
Step-by-step explanation:
the perpendicular bisector of BC passes through the midpoint of BC at right angles to BC.
calculate the slope m of BC using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = B (- 2, 1 ) and (x₂, y₂ ) = C (4, 2 )
[tex]m_{BC}[/tex] = [tex]\frac{2-1}{4-(-2)}[/tex] = [tex]\frac{1}{4+2}[/tex] = [tex]\frac{1}{6}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{6} }[/tex] = - 6
the midpoint of BC is the average of the x and y coordinates
midpoint = ( [tex]\frac{-2+4}{2}[/tex] , [tex]\frac{1+2}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex] , [tex]\frac{3}{2}[/tex] ) = ( 1, 1.5 )
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 6 , then
y = - 6x + c ← is the partial equation
to find c substitute (1, 1.5 ) into the partial equation
1.5 = - 6 + c ⇒ c = 1.5 + 6 = 7.5
y = - 6x + 7.5 ← equation of perpendicular bisector of BC
