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, it is in dropdown position, and is dropdown as the pre - image. it is dropdown to the pre - image

Explanation:

Step1: Analyze Translation and Dilation Effects on Orientation

Translations (sliding) and dilations (scaling) are rigid or similarity transformations that preserve orientation. So the orientation remains the same.

Step2: Analyze Position Change

First translation: 4 left, 7 up. Then dilation (doesn't change position relative to origin in terms of direction but scales distance from origin). Then translation 6 right. Net horizontal translation: \( -4 + 6=2 \) right, and vertical translation 7 up. So position is different from pre - image.

Step3: Analyze Size Change

Dilation with scale factor 2.5 (greater than 1) makes the image larger than the pre - image.

Step4: Analyze Congruence/Similarity

Since dilation (scale factor ≠1) is applied, the image is similar (not congruent) to the pre - image as similarity transformations include dilation, and congruence requires scale factor 1.

Answer:

• The final image has \(\boldsymbol{\text{the same}}\) orientation, it is in \(\boldsymbol{\text{a different}}\) position, and is \(\boldsymbol{\text{larger than}}\) the pre - image. It is \(\boldsymbol{\text{similar}}\) to the pre - image.