Question

Use the format below to write a sequence of rigid motions and dilation that takes square ABCD to square EFGH. Remember that corresponding points in the names of the figures need to correspond in your transformations.Your transformations should take this form: translate ___ by directed line segment __ which will take point _ to point _. Then, rotate the image using center _ by angle __. Finally, ___ by scale factor 2/5.

Answer 1

To map square ABCD onto square EFGH, one must perform a sequence of transformations: first a translation mapping a vertex of ABCD to a corresponding vertex of EFGH, followed by a rotation around this new vertex, and concluded by a dilation centered at the same vertex with a scale factor of 2/5.

Step-by-step explanation:

To perform the sequence of transformations that takes square ABCD to square EFGH, we need to define the translation, rotation, and dilation applied to the original square. The result will map each corresponding vertex of ABCD to the respective vertex of EFGH, following the order of corresponding points.

The general form of the answer would look like this:

1. 
   
3. Translate square ABCD by directed line segment XX' which will take point A to point E.
4. 
   
6. Rotate the image using center E by an angle of theta degrees.
7. 
   
9. Dilate the figure by a scale factor of 2/5 centered at point E.

Please note that the specific directed line segment, rotation angle, and center of the rotation would be determined based on the specific positions of squares ABCD and EFGH in your problem which are not provided here. However, in general, these steps represent the required sequence of transformations to map one square onto another using translation, rotation, and dilation.

Answer 2

Translate square ABCD by the direct line segment AE, which will take point A to point E. Then, rotate the image using center point A by angle 135° (=90°+45°). Finally, scale square ABCD by scale factor 2/5.