Answer:
Reflection across y axis
Translate up by 3 units
Step-by-step explanation:
Given
Required
Describe the transformation from f(x) to g(x)
First, take a reflection of f(x) across the y axis.
So f(x) becomes f(-x)
when reflected
Next, translate f(-x) up by 3 units to give g(x)
Where
Hence, the transformation from f(x) to g(x) includes:
Reflection across y axis
Translate up by 3 units
Since the given hexagon is a regular hexagon all it's sides will be of equal length. Now, we know that the Area of any regular hexagon is given by:
Where is the area of the regular hexagon
is the side length of the regular hexagon
Also, it's Perimeter is given by:
Thus, all that we need to do is to find the side length of any one of the sides and to do that let us have a look at at the data of vertices points given and find out which points are definitely adjacent to each other and are also easy to calculate.
A quick search will yield that D(8, 0) and E(4, 0) are definitely adjacent to each other.
Please check the attached file here for a better understanding of the diagram of the original regular hexagon. Points D and E indeed are adjacent to each other.
Let us now find the distance between the points D and E using the distance formula which is as:
Where is the distance.
and
are the coordinates of points D and E respectively. (please note that interchanging the values of the coordinates will not alter the distance
)
Applying the above formula we get:
We know that this distance is the side length of the given regular hexagon.
Now, if the sides of the given regular polygon are reduced by 40%, then the new length of the sides will be:
Thus, the area of the smaller hexagon will be:
unit squared
and the new smaller perimeter will be:
unit
Which are the required answers.
