Question

Which of the given sequence of transformations will produce an image similar but not congruent to the original figure?

• A. Clockwise rotation of ${15}^o$ and translation by 2 units toward the right
• B. Translation by 5 units up, reflection along the y-axis, and dilation with a scale factor of 1.5
• C. Dilation with a scale factor of 2 and then dilation with a scale factor of 0.5
• D. Reflection along the x-axis and the counterclockwise rotation of ${90}^o$

Answer 1

The correct option is B Translation by 5 units up, reflection along the y-axis, and dilation with a scale factor of 1.5

In option A: Clockwise rotation of ${15}^o$ and translation by 2 units toward the right
Rotation and translation are rigid transformations which conserve the measures of corresponding sides and angles and produce congruent as well as similar figures. Thus, this sequence of transformations will not produce a similar or congruent image and so it is incorrect.

In option B: Reflection along the x-axis and counterclockwise rotation of ${90}^o$
Reflection and rotation are rigid transformations which conserve the measures of corresponding sides and angles and produce congruent as well as similar figures. Thus, this sequence of transformations will not produce a similar or congruent image and so it is incorrect.

In option C: Translation by 5 units up, reflection along the y-axis, and dilation with a scale factor of 1.5
Translation and reflection are rigid transformations which conserve the measures of corresponding sides and angles and produce congruent as well as similar figures. After dilation with a scale factor of 1.5, the image will no longer be congruent, but it will still be similar indeed as the measure of angles does not change. Thus, this sequence of transformations will produce a similar, but not congruent image and so is correct.

In option D: Dilation with a scale factor of 2 and then dilation with a scale factor of 0.5
On dilation with a scale factor of 2, the side lengths of the image will become two times the length of the preimage.
And then dilation again with a scale factor of 0.5 will halve the side lengths of the image with double side lengths.
In this way, the figure will return to its original state that is similar and congruent to itself. Thus, this sequence of transformations will not produce a similar or congruent image and so is incorrect.

➡Option C is correct.