For the transformation to be defined as a rotation, which statements must be true? check all that apply. a. the segment connecting the center of rotation, c, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2). b. the transformation is rigid. c. every point on figure 1 moves through the same angle of rotation about the center of rotation, c, to create figure 2. d. segment cp is parallel to segment cp'. e. if figure 1 is rotated 360° about point c, it will be mapped onto itself.

The correct options are a, b, c and e.

Step-by-step explanation:

Rotation: In rotation, then figure is rotated about a point which is called center f rotation. This point stays fixed and everything else moves around that point in a circle.

The center of rotation is C.

If a point P lies on the preimage and P' is the corresponding point of P in the image, then the point P and P' are equidistant from center of rotation.

Option a is correct.

Rotation is a rigid transformation because the size and shape of the figure remains same.

Option b is correct.

Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.

Option c is correct.

If angle of rotation is 90°, then CP⊥CP'. For all rotation CP is not parallel to CP'.

Option d is incorrect.

Any figure is rotated 360° about the center, then it will mapped onto itself.

If figure 1 is rotated 360° about point C, it will be mapped onto itself.

Option e is incorrect.

Therefore the correct options are a, b, c and e.

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.