Question

1. 1)liam draws a rectangle on a coordinate grid. he then performs the following transformations in the order below: a rotation of 90° clockwise a reflection across the y-axis a dilation by a factor of 2 a translation 4 units down he claims the resulting square is congruent to the original square. which of liam’s four transformations should he not have done in order for his claim to be correct? ∘ a dilation by a factor of 2 ∘ a translation 4 units down ∘ a reflection across the y-axis ∘ a rotation of 90° clockwise

Explanation:

To determine which transformation makes the figure non - congruent, we recall the definitions of congruence - preserving (rigid) and non - congruence - preserving transformations. Rigid transformations (rotation, reflection, translation) preserve the size and shape of a figure, so congruence is maintained. Dilation is a non - rigid transformation as it changes the size of the figure (scales it by a factor). A dilation by a factor of 2 will make the resulting figure (after dilation) have double the side length of the original, so it will not be congruent. Rotation, reflection, and translation do not change the size or shape, so they preserve congruence.

Answer:

A. a dilation by a factor of 2