Question

△abc undergoes three transformations: - it is translated 4 units left and 7 units up. - then it is dilated, centered at the origin using a scale factor of 2.5. - finally it is translated 6 units right. use the drop - down menus to correctly complete the statements. the final image has dropdown orientation, is in dropdown position, and is dropdown size as the pre - image. it is dropdown but also dropdown to the pre - image.

Explanation:

Step1: Analyze Orientation

Translations and dilations (centered at origin, scale factor >0) preserve orientation. So the final image has the same orientation as the pre - image.

Step2: Analyze Position

First translation: 4 units left and 7 units up. Then dilation (doesn't change position relative to origin in terms of translation effect, just scales). Then translation 6 units right. Net horizontal translation: - 4+6 = 2 units right. Vertical translation: 7 units up. So the position is different from the pre - image (moved right and up).

Step3: Analyze Size

Dilation with scale factor 2.5 (which is greater than 1) makes the image larger. So the final image is larger in size than the pre - image.

Step4: Analyze Similarity and Congruence

Dilation changes the size, so the image is similar (same shape, different size) but not congruent (congruent requires same size and shape) to the pre - image.

Answer:

The final image has the same orientation, is in a different position, and is larger in size as the pre - image. It is similar but also not congruent to the pre - image.

(For the drop - down menus, assuming the options for orientation are "the same" / "different", for position "the same" / "different", for size "the same as" / "larger than" / "smaller than", for the last two "similar" / "congruent" and "not congruent" / "not similar" respectively, the answers would be: the same, different, larger than, similar, not congruent)