Respuesta :

semsee45

Answer:

[tex]\sqrt{74}[/tex]

Step-by-step explanation:

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{let}\:(x_1,y_1)=(2,-6)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(7,1)[/tex]

[tex]d=\textsf{length of segment AB}[/tex]

Substituting points into the distance formula and solving for d:

[tex]\implies d=\sqrt{(7-2)^2+(1-(-6))^2}[/tex]

[tex]\implies d=\sqrt{5^2+7^2}[/tex]

[tex]\implies d=\sqrt{25+49}[/tex]

[tex]\implies d=\sqrt{74}[/tex]

LENGTH

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[tex] \large \sf \underline{Answer:}[/tex]

[tex] \qquad\qquad \qquad \huge \bold{\sqrt{74} }[/tex]

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[tex] \large \sf \underline{Solution:}[/tex]

Solving;

  • [tex] \sf{D=\sqrt{(7-2)^2+(1-(-6))^2}}[/tex]

  • [tex] \sf{D=\sqrt{5^2+7^2}}[/tex]

  • [tex] \sf{D=\sqrt{25+49}}[/tex]

  • [tex] \sf \underline {\pmb{D=\sqrt{74}}}[/tex]

Hence, the length of segment AB is √74.

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