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Ivahew [28]
3 years ago
12

Line segment EF is shown on a coordinate grid: A coordinate plane is shown. Line segment EF has endpoints negative 3 comma 2 and

negative 1 comma 2. The line segment is rotated 180 degrees counterclockwise about the origin to form E'F'. Which statement describes E'F'? E'F' is perpendicular to EF. E'F' and EF are equal in length. E'F' is half the length of EF. E'F' is greater than twice the length of EF.
Mathematics
1 answer:
iren [92.7K]3 years ago
6 0

Answer:

The answer is " E'F' and EF are equal in length".

Step-by-step explanation:

By rotating that through some degree, a revolution is some kind of rigid transformation, which creates an image of the very same shape and size. There will be two main properties of the rotation:

  • Preservation of rotating scale (including sides and angles).
  • The lines connecting the rotation center to the pre-image and the corresponding image point are of equal length.

In each line, the segment is rotated counterclockwise 180 degrees around the origin to form E'F, that's why the above given choice is correct.

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Solve the proportions:
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<u>Answer:</u>

  • 6. 6.75
  • 7. 27
  • 8. 92/17
  • 9. 49

<u>Step-by-step explanation:</u>

<u>- Question 6 -</u>

  • 9/16 = x/12
  • => 16x = 12 x 9
  • => 16x = 108
  • => x = 6.75

Hence, <u>the value of x in this proportion is 6.75.</u>

<h3>_______________________________</h3>

<u>- Question 7 -</u>

  • -3 + x/18 = 12/9
  • => -3/18 + x/18 = 4/3
  • => x/18 = 4/3 + 1/6
  • => x/18 = 8/6 + 1/6
  • => x/18 = 9/6
  • => x = 9/6 x 18
  • => x = 27

Hence, <u>the value of x is 27</u>

<h3>_______________________________</h3>

<u>- Question 8 -</u>

17/15 = 10/2x - 2

=> 17(2x - 2) = 150

=> 34x - 34 = 150

=> 34x = 184

=> x = 184/34

=> x = 92/17

Hence, <u>the value of x is 92/17</u>

<h3>_______________________________</h3>

<u>- Question 9 -</u>

  • x - 16/x + 6 = 3/5
  • => 5(x - 16) = 3(x + 6)
  • => 5x - 80 = 3x + 18
  • => 2x = 98
  • => x = 49

Hence, <u>the value of x is 49.</u>

<h3>_______________________________</h3>

Hoped this helped.

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