Write a function rule using function notation that will transform a geometric figure by a dilation of 3.

A. [tex]f(x, y)=(-3 x,-3 y)[/tex]
B. [tex]f(x, y)=(3 x, 3 y)[/tex]
C. [tex]f(x, y)=(3 x, y)[/tex]
D. [tex]f(x, y)=(x, 3 y)[/tex]

The function rule that represents a dilation of 3 is f ( x , y ) = ( 3 x , 3 y ) . This transformation enlarges each point of a geometric figure by a factor of 3. Therefore, the correct multiple choice option is B.
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Answered by Anonymous | 2025-07-07

Understand that a dilation of 3 scales both x and y coordinates by a factor of 3.
Apply the dilation factor to a point (x, y) resulting in (3x, 3y).
Express the transformation as a function rule.
The function rule for a dilation of 3 is: f ( x , y ) = ( 3 x , 3 y ) ​

Explanation

Understanding Dilation The problem asks us to find the function rule that represents a dilation of 3. A dilation is a transformation that changes the size of a geometric figure, either enlarging it (if the scale factor is greater than 1) or shrinking it (if the scale factor is between 0 and 1). In this case, the dilation factor is 3, which means the figure will be enlarged by a factor of 3.

Applying the Dilation Factor A dilation of 3 means that every point (x, y) on the original figure will be transformed to a new point where both the x-coordinate and the y-coordinate are multiplied by 3. So, the new coordinates will be (3x, 3y).

The Function Rule Therefore, the function rule that represents a dilation of 3 is f ( x , y ) = ( 3 x , 3 y ) .


Examples
Imagine you have a photograph and you want to enlarge it. If you apply a dilation of 3 to the photograph, it means you are making the photograph three times larger in both width and height. This is similar to how a projector works, where it takes a small image and projects a larger version onto a screen.

Answered by GinnyAnswer | 2025-07-07