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ehidna [41]
2 years ago
8

A figure is located at (0, 0), (−3, −4), and (−3, 0) on a coordinate plane. What kind of 3-D shape would be created if the figur

e was rotated around the x-axis? Provide an explanation and proof of your answer to receive full credit. Include the dimensions of the 3-D shape in your explanation.
Mathematics
1 answer:
AysviL [449]2 years ago
8 0

Answer:

cone

Step-by-step explanation:

Define the given points:

  • A = (0, 0)
  • B = (-3, -4)
  • C = (-3, 0)

As two points have the same x-coordinate and two different points have the same y-coordinate, the <u>2D shape</u> the points make is a right triangle (see first attached diagram).

As points B and C lie on the <u>same vertical line</u> (x = -3), and point C lies on the x-axis, <u>rotating</u> line segment BC about the x-axis will produce a circle with center C and radius BC (4 units).

As point A lies on the x-axis, it will <u>not move</u> when rotated about the x-axis.

Therefore, the 3D shape the triangle will create is a cone with:

  • vertex at (0, 0)
  • center of circular base at (-3, 0)
  • radius of circular base of 4 units
  • height of 3 units

(see second attached diagram)

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