Answer:
[tex]\frac{2\sqrt{61} }{3}[/tex]
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A(1, 4) and (x₂, y₂ ) = B(- 3, [tex]\frac{2}{3}[/tex] )
AB = [tex]\sqrt{(-3-1)^2+(\frac{2}{3}-4)^2 }[/tex]
= [tex]\sqrt{(-4)^2+(-10/3)^2}[/tex]
= [tex]\sqrt{16+100/9}[/tex]
= [tex]\sqrt{144/9+100/9}[/tex]
= [tex]\sqrt{\frac{244}{9} }[/tex]
= [tex]\sqrt{\frac{4(61)}{9} }[/tex]
= [tex]\frac{2\sqrt{61} }{3}[/tex]
