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 the same orientation, is in a different position,
and is not the same size size as the pre - image.
it is similar but also drop - down menu to the pre - image.
drop - down menu options: congruent, not congruent

Explanation:

Step1: Analyze Transformations' Effects

• Translation: Shifts position, preserves orientation and size.
• Dilation (scale factor 2.5): Changes size (scales by 2.5), preserves orientation (center at origin, dilation is uniform), but makes it non - congruent (since size changes).
• Final Translation: Shifts position again.

Step2: Evaluate Orientation

Translations and dilation (with center at origin) do not change the orientation of the figure. So orientation is the same.

Step3: Evaluate Position

Two translations (4 left +7 up, then 6 right) and a dilation (which doesn't change position relative to the origin in terms of the transformation's effect on position change from translations) result in a different position from the pre - image.

Step4: Evaluate Size

Dilation with scale factor 2.5 changes the size, so it is not the same size.

Step5: Evaluate Congruence

Congruent figures must have the same size and shape. Since the size changed (due to dilation), the final image is similar (same shape, different size) but not congruent.

Answer:

For the last drop - down (the one with "congruent" and "not congruent" options), the answer is "not congruent". The other filled - in options are correct as: orientation - the same; position - a different; size - not the same size; similarity - similar and then not congruent.