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A is the point (-2,4) and B is the point (7,1). Find the length of AB giving your answer in its simplest surd form.​

Sagot :

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]

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