Answer:
The slope of the line segment CD is ( - [tex]\frac{8}{9}[/tex] )
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
Coordinates of the midpoint are
( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
The slope of a line segment with coordinates of the ends
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
is m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
~~~~~~~~~~~~~
Point D is the midpoint of a segment AB
A ( 4 , 12 )
B ( - 6 , - 8 )
( [tex]\frac{-6+4}{2}[/tex] , [tex]\frac{-8+12}{2}[/tex] ) = ( - 1 , 2 )
D ( - 1 , 2 )
C ( 8 , - 6 )
[tex]m_{CD}[/tex] = [tex]\frac{-6-2}{8-(-1)}[/tex] = - [tex]\frac{8}{9}[/tex]
