Question

1. reflect the figure over the x - axis. then, mark the statements as true or false

i the corresponding sides in the pre - image and image are congruent.
i the reflection changed the orientation of the vertices.

1. translate the figure 8 units left and 2 units up. then, mark the statements as true or false

i the pre - image is located in quadrant iii.
i the pre - image and image are congruent figures.

1. rotate the figure 90° clockwise. then, mark the statements as true or false

i the orientation of the figure did not change.
i the corresponding angle measures in the pre - image and image are congruent.

1. dilate the figure by a scale factor of 2.5. then, mark the statements as true or false

i the orientation of the figure did not change.
i the pre - image and image are congruent figures.

Explanation:

Step1: Recall properties of transformations

• Reflection over x - axis: A reflection is a rigid transformation. Rigid transformations preserve side - lengths and angle - measures. So, for a reflection over the x - axis, the corresponding sides in the pre - image and image are congruent. Also, the orientation of the vertices changes.
• Translation: A translation is a rigid transformation. It moves the figure without changing its shape, size, or orientation. So, the pre - image and image are congruent, and the orientation of the figure does not change.
• Rotation: A 90° clockwise rotation changes the orientation of the figure. But it is a rigid transformation, so the corresponding angle measures in the pre - image and image are congruent.
• Dilation: A dilation with a scale factor other than 1 changes the size of the figure. So, the pre - image and image are not congruent, and the orientation of the figure does not change (if the center of dilation is the origin and no rotation is involved in the dilation process).

Step2: Analyze each statement

For reflection over x - axis:

• "The corresponding sides in the pre - image and image are congruent." is True because reflection is a rigid transformation.
• "The reflection changed the orientation of the vertices." is True.

For translation 8 units left and 2 units up:

• "The pre - image is located in Quadrant III" (information not sufficient in the question to determine this precisely from the given text, assuming we focus on the general properties).
• "The pre - image and image are congruent figures." is True because translation is a rigid transformation.

For 90° clockwise rotation:

• "The orientation of the figure did not change." is False.
• "The corresponding angle measures in the pre - image and image are congruent." is True because rotation is a rigid transformation.

For dilation by a scale factor of 2.5:

• "The orientation of the figure did not change." is True (assuming standard dilation with no additional rotation).
• "The pre - image and image are congruent figures." is False because dilation changes the size of the figure.

Answer:

• Reflection over x - axis:
• "The corresponding sides in the pre - image and image are congruent." True
• "The reflection changed the orientation of the vertices." True
• Translation 8 units left and 2 units up:
• "The pre - image and image are congruent figures." True
• 90° clockwise rotation:
• "The orientation of the figure did not change." False
• "The corresponding angle measures in the pre - image and image are congruent." True
• Dilation by a scale factor of 2.5:
• "The orientation of the figure did not change." True
• "The pre - image and image are congruent figures." False