Question

a series of transformations were applied to rectangle hijk to create rectangle pqrs. if rectangle pqrs is congruent to rectangle hijk, which of the following transformations could have been applied to rectangle hijk? i. a dilation ii. a reflection iii. a rotation iv. a translation a. ii and iii only b. i, ii, iii, and iv c. ii and iv only d. ii, iii, and iv only

Explanation:

• Dilation: A dilation changes the size of a figure. If the scale factor is not \(1\), the figure after dilation will not be congruent to the original figure. So, a dilation (I) cannot be part of the transformations if the two rectangles are congruent.
• Reflection: A reflection is a rigid transformation. It flips a figure over a line, but the size and shape of the figure remain the same. So, a reflection (II) can be part of the transformations.
• Rotation: A rotation is a rigid transformation. It turns a figure around a point, and the size and shape of the figure do not change. So, a rotation (III) can be part of the transformations.
• Translation: A translation is a rigid transformation. It slides a figure, and the size and shape of the figure remain unchanged. So, a translation (IV) can be part of the transformations.

Answer:

D. II, III, and IV only