The transformation of a shape includes rotating and reflecting the shape;
- The image of BC after [tex]120^o[/tex] is FA
- The image of BC reflecting over FC is DC.
(a) Image of BC after [tex]120^o[/tex] rotation
First, we calculate the angle of rotation, to make the hexagon lie onto itself
[tex]\alpha = \frac{\theta}{n}[/tex]
Where:
[tex]\theta = 360^o[/tex] --- angle at the center of the hexagon and the circle
[tex]n = 6[/tex] -- sides of hexagon
So, we have:
[tex]\alpha = \frac{360^o}{6}[/tex]
[tex]\alpha = 60^o[/tex]
This means that a [tex]60^o[/tex] rotation would make the hexagon lie onto itself.
We have that:
[tex]120^o = 60^o \times 2[/tex]
This means that the shape can be rotated [tex]60^o[/tex] twice to achieve the [tex]120^o[/tex] rotation.
The image of BC at the first [tex]60^o[/tex] rotation is AB
The image of BC at the next [tex]60^o[/tex] rotation is FA
Hence, the image of BC after [tex]120^o[/tex] is FA
(b) Image of BC after reflection over line FC
Line FC divides the hexagon into equal halves.
So, when reflected over line FC, each segment would be flipped on the opposite segment.
The opposite of segment BC is DC.
Hence, the image of BC reflecting over FC is DC.
Read more about transformations at:
https://brainly.com/question/11707700
