collinsdessie8101 collinsdessie8101
  • 07-09-2018
  • Mathematics
contestada

A line segment has endpoint (5,4,3) and (1,6,-9) find it length and the midpoint g

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DeanR
DeanR DeanR
  • 07-09-2018

Its squared length is given by the Pythagorean Theorem:

[tex]d^2 = (5-1)^2 + (4-6)^2 + (3 - -9)^2 = 16 + 4 + 144 = 164[/tex]

[tex]d = \sqrt{164} = 2\sqrt{41}[/tex]

Answer: 2√41

The midpoint is the average of each coordinate:

[tex]G(x,y,z) = \left( \dfrac{5 + 1}{2}, \dfrac{4 + 6}{2}, \dfrac{3 + -9}{2} \right) = (3, 5, -3)[/tex]

Answer: (3, 5, -3)


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