Question

Which rules represent a transformation that maps one shape onto to another to establish their congruence? Select all that apply.

A. A dilation by a scale factor of 3 about the origin.
B. A translation to the right 2 and down 6.
C. A reflection across the line y = 2.
D. A counter-clockwise rotation of 90 degrees about the origin.
E. A horizontal wretch by a factor of 2 about the origin.

Answer 1

The rules that represent transformations for congruence are translation (option B), reflection across a line (option C), and rotation around a point (option D), because they do not change the size or shape of the original figure.

Step-by-step explanation:

The rules that represent a transformation mapping one shape onto another to establish their congruence while maintaining size and shape are:

• Translation: Moving the shape without rotating or flipping it. An example would be 'A translation to the right 2 and down 6', which corresponds to option B.
• Reflection: Flipping the shape across a line, like a mirror image. An example would be 'A reflection across the line y = 2', corresponding to option C.
• Rotation: Turning the shape around a fixed point. An example is 'A counter-clockwise rotation of 90 degrees about the origin', represented by option D.

However, a dilation by a scale factor of 3 or a horizontal stretch by a factor of 2 will both change the size of the shape, therefore, they do not establish congruence between the original and the transformed shapes. Hence, options A and E are excluded.