Answer:
Option C is correct
unit and
unit
Step-by-step explanation:
Area of a rectangle is given by:
....[1]
where
A is the area of rectangle
l is the length of a rectangle
w is the width of a rectangle.
As per the statement:
A certain rectangle has an area of
⇒
Now factor this trinomial :
⇒
⇒ unit square
On comparing with [1] we have;
unit and
unit
Therefore,the length and width of the rectangle are:
unit and
unit
Note: The image of G after the dilation must be G'(5,-5) instead of G'(5,5).
Given:
The vertices of a rectangle are E(4,8), F(2,8), G(2,-2) and H(-4,-2).
The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,-5).
To find:
The algebraic representation that represents this dilation.
Solution:
If a figure is dilated by factor k with origin as the center of dilation, then the dilation is defined as:
...(i)
Let the given rectangle is dilated by factor k with origin as the center of dilation. Then,
The image of G after dilation is G'(5,-5). So,
On comparing both sides, we get
So, the scale factor is .
Substituting in (i), we get
Therefore, the required algebraic representation to represents this dilation is .