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If the legs of each triangular base are 5 cm and 3 cm and the height of the prism is 4 cm, what
are the coordinates of the vertices of the prism?

Respuesta :

xero099

The coordinates of the six vertices of the prism are listed below:

  1. [tex](x_{1},y_{1}, z_{1}) = (0, 0, 0)\,[ft][/tex]
  2. [tex](x_{2}, y_{2}, z_{2}) = (0, 0, 5)\,[ft][/tex]
  3. [tex](x_{3}, y_{3}, z_{3}) = (3, 0, 0)\,[ft][/tex]
  4. [tex](x_{4}, y_{4}, z_{4}) = (0, 4, 5)\,[ft][/tex]  
  5. [tex](x_{5}, y_{5}, z_{5}) = (0, 4, 0)\,[ft][/tex]
  6. [tex](x_{6}, y_{6}, z_{6}) = (3, 4, 0)\,[ft][/tex]

The number of vertices of a prism with a polygonal base ([tex]n[/tex]) is described by the following expression:

[tex]n = 2\cdot s[/tex] (1)

Where [tex]s[/tex] is the number of sides of the base.

If we know that [tex]s = 3[/tex], then the number of vertices of the prism are:

[tex]n = 2\cdot 3[/tex]

[tex]n = 6[/tex]

A prism with triangular base has six vertices, let suppose that the triangle of the base is right-angled. and coincides with a right-hand rectangular coordinate system. Then, we can conclude that the coordinates of the six vertices are the following:

  1. [tex](x_{1},y_{1}, z_{1}) = (0, 0, 0)\,[ft][/tex]
  2. [tex](x_{2}, y_{2}, z_{2}) = (0, 0, 5)\,[ft][/tex]
  3. [tex](x_{3}, y_{3}, z_{3}) = (3, 0, 0)\,[ft][/tex]
  4. [tex](x_{4}, y_{4}, z_{4}) = (0, 4, 5)\,[ft][/tex]  
  5. [tex](x_{5}, y_{5}, z_{5}) = (0, 4, 0)\,[ft][/tex]
  6. [tex](x_{6}, y_{6}, z_{6}) = (3, 4, 0)\,[ft][/tex]

We kindly invite to check this question on prisms: https://brainly.com/question/8828506

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