Line segment ef is shown on a coordinate grid: the line segment is rotated 180 degrees counterclockwise about the origin to form e'f'. which statement describes e'f'? a e'f' is perpendicular to ef.b e'f' and ef are equal in length.c e'f' is half the length of ef.d e'f' is greater than twice the length of ef.

B. E'F' and EF are equal in length.

Step-by-step explanation:

The rotation has two main properties:-

1. Rotations preserve size ( includes sides and angles).

2. Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.

Given : The line segment is rotated 180 degrees counterclockwise about the origin to form E'F'.

Then, E'F' and EF are equal in length. ( by property 1.)

The common ratio of the first G.P. series will be the cube root of the common ratio of the second G.P. series.

Step-by-step explanation:

Let us assume that the first series has first term a and the common ratio r and  is given by  

a, ar, ar², ar³, ......... up to infinite terms

It is given that the terms of the second series are a cube of the corresponding terms of the first series.

So, the second series is up to infinite terms.

So, it is clear that the second series is a G.P. series with first term a³ and common ratio r³.

Therefore, the common ratio of the first G.P. series will be the cube root of the common ratio of the second G.P. series. (Answer)