Question

Which sequence of transformations would create an image that is incongruent to the original pre-image? O A translation 4 units to the left followed by a dilation by 2 O A rotation of 90- followed by a translation of 2 units to the right O A reflection across the y-axis followed by a rotation of 180- O A rotation of 270 followed by a reflection across the x-axis.​

Answer 1

Answer: Choice A

A translation 4 units to the left followed by a dilation by 2

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Step-by-step explanation:

The following transformations will make the pre-image and image congruent to one another:

• Reflection
• Rotation
• Translation

If you apply any of those transformations mentioned above, then the image is an identical copy of the pre-image. Nothing about the figure has changed other than it has been shifted, rotated, or reflected in some way. The figure retains its original size and shape. These transformations are called isometries.

A dilation on the other hand does not preserve the size. "Dilation by 2" means the scale factor is 2, so the image will be twice as large compared to the pre-image, in terms of linear dimension. This means there is no way the image is congruent to the pre-image if a dilation has occurred.

Based on all this, choice A is the answer. Choices B, C, and D only involve the three isometries mentioned earlier and no dilation at all, so they can be ruled out.