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Which sequence of transformations would result in a figure that is similar, but not congruent, to the original figure?

Select all that apply.

A.a dilation with a scale factor of 1.9 followed by a rotation of –30°
B.a dilation with a scale factor of 0.1 followed by a translation of 5 units left
C.a reflection across the y-axis followed by a dilation with a scale factor of 10
D.a rotation about the origin of 65° followed by a reflection across the x-axis

Respuesta :

The correct answers are:

A.a dilation with a scale factor of 1.9 followed by a rotation of –30° ; B.a dilation with a scale factor of 0.1 followed by a translation of 5 units left ; and C.a reflection across the y-axis followed by a dilation with a scale factor of 10

Explanation:

A dilation shrinks or stretches a figure.  This means it creates a figure that is similar to, but not congruent to, the original figure.  All of the figures with dilations will be similar but not congruent to the original figure.

The resultant figure is similar but not congruent, to the original figure in the first three cases which are A, B, and C.

Transformation are of four types for a 2-D shapes.

  • Translation
  • Rotations
  • Reflections
  • Dilation

  • A- A dilation with a scale factor of 1.9 followed by a rotation of –30° In this case the original shape will be rotated anticlockwise which will not affect the size and shape of the original shape but multiplied by the scale factor of 1.9 hence the shape will be changed and the shape will remain same. Hence in this case the original figure is similar but not congruent.
  • B. A dilation with a scale factor of 0.1 followed by a translation of 5 units left. In this case the original figure is again multiplied by the scale factor 0.1 and transect by 5 units which will only change its size but not shape. Hence in this case the original figure is similar but not congruent.

  • C. A reflection across the y-axis followed by a dilation with a scale factor of 10- In the the above case the original figure is reflected to the y-axis and change its size with scale factor of 10. Hence in this case the original figure is similar but not congruent.

  • D. A rotation about the origin of 65° followed by a reflection across the x-axis In this case the original figure is reflected across the x-axis and rotated 65 degrees about the origin. This will only change the orientation but not the size and shape of the original figure. Hence in this case the original figure is similar as well as congruent.

Hence, the resultant figure is similar but not congruent, to the original figure in the first three cases which are A, B, and C.

For more about the transformation, follow the link below-

https://brainly.com/question/11709244

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