Answer:
AB = 3[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Calculate AB using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (- 2, 4) and (x₂, y₂ ) = B (7, 1 )
AB = [tex]\sqrt{(7-(-2))^2+(1-4)^2}[/tex]
= [tex]\sqrt{(7+2)^2+(-3)^2}[/tex]
= [tex]\sqrt{9^2+9}[/tex]
= [tex]\sqrt{81+9}[/tex]
= [tex]\sqrt{90}[/tex]
= [tex]\sqrt{9(10)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{10}[/tex]
= 3[tex]\sqrt{10}[/tex]
