Transformation of Triangle ΔCDE to ΔKIJ

A figure is shown.

image.png

If ΔCDE is transformed first by the algebraic rule (x, y)→(−x, y) and then by the rule (x, y)→(2x, 2y) to create ΔKIJ , which of the figures below correctly shows the transformation?

A

image.png

B

image.png

C image.png

D image.png

A

B

C

D

To determine which figure correctly shows the transformation of triangle ( \Delta CDE ) to triangle ( \Delta KIJ ) using the specified algebraic rules, we need to analyze the transformations step by step.

1. First Transformation: (x, y) → (−x, y)
   This transformation reflects the triangle across the y-axis. Each point ( (x, y) ) in triangle ( \Delta CDE ) will be transformed to ( (-x, y) ).

2. Second Transformation: (x, y) → (2x, 2y)
   This transformation scales the triangle by a factor of 2. Each point ( (x, y) ) will be transformed to ( (2x, 2y) ).

Now, let's apply these transformations to a generic point ( (x, y) ):

• After the first transformation, the point becomes ( (-x, y) ).
• After the second transformation, it becomes ( (2(-x), 2y) = (-2x, 2y) ).

This means that the final coordinates of each point in triangle ( \Delta KIJ ) will be the result of reflecting the original triangle across the y-axis and then scaling it by a factor of 2.

To find the correct figure among the options A, B, C, and D, you would need to look for a triangle that is:

• Reflected across the y-axis (the x-coordinates of the points should be negative).
• Scaled such that the distances from the origin are doubled compared to the original triangle.

Since I cannot see the images, I recommend checking each option against these criteria to identify which one correctly represents the transformations applied to triangle ( \Delta CDE