Answer:
all [tex]\sqrt{89}[/tex]
Step-by-step explanation:
Calculate the lengths using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = J(- 2, - 2) and (x₂, y₂ ) = J'(3, 6)
JJ' = [tex]\sqrt{(3+2)^2+(6+2)^2}[/tex] = [tex]\sqrt{5^2+8^2}[/tex] = [tex]\sqrt{25+64}[/tex] = [tex]\sqrt{89}[/tex]
Repeat with
(x₁, y₁ ) = K(- 8, - 4) and (x₂, y₂ ) = K'(- 3, 4)
KK' = [tex]\sqrt{(-3+8)^2+(4+4)^2}[/tex] = [tex]\sqrt{5^2+8^2}[/tex] = [tex]\sqrt{25+64}[/tex] = [tex]\sqrt{89}[/tex]
Repeat with
(x₁, y₁ ) = L(- 6, - 6) and (x₂, y₂ ) = L'(- 1, 2)
LL' = [tex]\sqrt{(-1+6)^2+(2+6)^2}[/tex] = [tex]\sqrt{5^2+8^2}[/tex] = [tex]\sqrt{25+64}[/tex] = [tex]\sqrt{89}[/tex]
