We will begin by reflecting the preimage over the y-axis. To do so, we will apply the Coordinate Rules for Reflections. Let's recall the rule, especially the one about reflection over the y-axis!
The Coordinate Rule for Reflection Over the y-Axis
If (a,b) is reflected in the y- axis, then its image is the point (-a,b).
With this information, we will reflect each vertex of â–ł DEF over the y-axis.
(a,b) → (-a,b)
D(-3,6) → D'(3,6)
E(-3,3) → E'(3,3)
F(-9,3) → F'(9,3)
Now, we will draw the image of reflection, â–ł D'E'F'.
Next, we will reduce â–ł D'E'F' with a scale factor of 13. To do so we will multiply the coordinates of each vertex by 13. This transformation is called dilation with a scale factor of 13. Note that by the Coordinate Rule for Dilation the center of dilation is at the origin, (0,0).
(x,y) → (13x,13y)
D'(3,6) → P(1,2)
E'(3,3) → Q(1,1)
F'(9,3) → R(3,1)
Finally, we have transformed â–ł DEF to â–ł PQR.
Therefore, the similarity transformation is a reflection over the y-axis and then a dilation with a scale factor of 13. Take note that this is just one possible way of doing the similarity transformation, and your answer may vary.
