Question

Figure

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Which combinations of transformations will always produce congruent figures? Check all that apply.
a dilation, followed by a rotation
a reflection, followed by a dilation
a rotation, followed by a translation
a translation, then a rotation, followed by a stretch
O a translation, followed by two reflections
O O O O O

Answer 1

• a rotation, followed by a translation
• a translation, followed by two reflections

Explanation:

The rigid motions are the transformations that produce congruent images.

There are three main kinds of rigid motions :

• Reflections : Flips a figure across a line of reflection.
• Rotations : Rotates a figure about some degrees around a center point.
• Translations : Moves figure on a plane about some distance in a certain direction.

But dilation is not a rigid transformation because it may change the size of the image. It is usually used to shrink or enlarge a shape.

So, the options having dilation and term "stretch" cannot produce congruent figures.

Hence, the correct options are :

• a rotation, followed by a translation
• a translation, followed by two reflections