Question

a transformation is applied to a figure to create a new figure on a coordinate grid. which transformation does not preserve congruence?
a rotation of 270 degrees counterclockwise
a reflection across the y - axis
a dilation by a scale factor of 1.5
a translation of 50 units down.

Explanation:

Step1: Recall properties of transformations

• Rotation: A rotation (like \(270^{\circ}\) counter - clockwise) is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, the pre - image and the image are congruent.
• Reflection: A reflection (across the \(y\) - axis) is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, the pre - image and the image are congruent.
• Dilation: A dilation with a scale factor \(k

eq1\) changes the size of the figure. If \(k = 1.5>1\), the image is larger than the pre - image. Congruent figures must have the same size.

• Translation: A translation (50 units down) is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, the pre - image and the image are congruent.

Answer:

A dilation by a scale factor of \(1.5\)