Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Midpoint of a line segment joining points [tex](x,y)[/tex] and [tex](u,v)[/tex] is given by [tex](\frac{x+u}{2},\frac{y+v}{2} )[/tex]
Points are R(-1,10),S(5,4)and T (-4,-2).
Midpoint of RS = [tex](\frac{-1+5}{2},\frac{10+4}{2} )=(\frac{4}{2},\frac{14}{2} )=(2,7 )[/tex]
Midpoint of RT = [tex](\frac{-1-4}{2},\frac{10-2}{2} )=(\frac{-5}{2},\frac{8}{2} )=(\frac{-5}{2},4)[/tex]
Slope of a line joining points [tex](a,b)[/tex] and [tex](c,d)[/tex] is given by [tex]\frac{d-b}{c-a}[/tex]
Slope of line joining midpoints of side RS and RT = [tex](\frac{4-7}{\frac{-5}{2}-2 })=(\frac{-3}{\frac{-9}{2} })=\frac{2}{3}[/tex]
