kellerpaula kellerpaula
  • 22-03-2020
  • Mathematics
contestada

Trigonometry
Length of line segment
Find the length of the line segment whose endpoints are: (2, 3) and (6, -7)

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Ben
Ben Ben
  • 22-03-2020

[tex]\huge\boxed{2\sqrt{29}}[/tex]

Use the distance formula:

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

Substitute in the known values.

[tex]d=\sqrt{(6-2)^2+(-7-3)^2}[/tex]

Subtract.

[tex]d=\sqrt{4^2+(-10)^2}[/tex]

Find the powers.

[tex]d=\sqrt{16+100}[/tex]

Add.

[tex]d=\sqrt{116}[/tex]

Find two factors of [tex]116[/tex].

[tex]d=\sqrt{4*29}[/tex]

Find the two factors of [tex]4[/tex].

[tex]d=\sqrt{2*2*29}[/tex]

Move the pair outside the square root.

[tex]d=\boxed{2\sqrt{29}}[/tex]

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