Question

27
what is the rule for the transformation above?
a. (x,y)=(-2x,-2y)
b. (x,y)=(2x,-2y)
c. (x,y)=(-2y,2x)

Explanation:

Step1: Analyze point - transformation

Let's take a point on the original figure, say a vertex. Suppose a vertex of the original green - shaped figure is \((x,y)\). We need to find its corresponding point \((x',y')\) on the new figure and check which transformation rule holds.

Step2: Check option A

If \((x',y')=(- 2x,-2y)\), this represents a dilation by a factor of 2 and a rotation of 180 degrees about the origin. But the orientation of the figure in the given transformation is not a 180 - degree rotation.

Step3: Check option B

If \((x',y')=(2x,-2y)\), this is a dilation by a factor of 2 in the x - direction and a reflection across the x - axis and dilation by a factor of 2 in the y - direction. This does not match the given transformation.

Step4: Check option C

Let's assume a point \((x,y)\) on the original figure. For the transformation \((x',y')=(-2y,2x)\), this represents a rotation of 90 degrees counter - clockwise about the origin and a dilation by a factor of 2. If we take a vertex of the original figure and apply the rule \((x',y')=(-2y,2x)\), we can see that it matches the transformation of the green - shaped figure from the left to the right graph.

Answer:

C. \((x',y')=(-2y,2x)\)