A specialized camera produces a photograph that is 1.5 inches by 4 inches. This photograph is enlarged using a scale factor of 3. The resulting image is then enlarged for printing using a scale factor of 2.

Answer 1

To find the final dimensions of the photograph after both enlargements, we can follow these steps:

1. Initial Photograph Dimensions:

   • Width = 1.5 inches
   • Height = 4 inches

2. First Enlargement (scale factor of 3):

   • New Width = 1.5 inches × 3 = 4.5 inches
   • New Height = 4 inches × 3 = 12 inches

3. Second Enlargement (scale factor of 2):

   • New Width = 4.5 inches × 2 = 9 inches
   • New Height = 12 inches × 2 = 24 inches

Thus, after both enlargements, the final dimensions of the photograph are 9 inches by 24 inches.

Answer 2

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Part 1 of 2
(a) Which sequence(s) of transformations will map Figure A onto Figure B exactly

Answer 3

To determine the sequence of transformations that map Figure A onto Figure B, we generally consider geometric transformations such as translations, rotations, reflections, and dilations. However, specific details about Figures A and B, including their coordinates, shapes, and orientations, are necessary to provide an accurate answer.

Since I don’t have access to the visual elements or coordinates for Figures A and B based on the input provided, here’s a guideline on how to approach this problem:

1. Identify Key Features: Look at corners, edges, and any markings in Figure A and Figure B. Identify the key points that can help in matching them.

2. Translation: Check if you can slide Figure A horizontally or vertically to match Figure B.

3. Rotation: Determine if rotating Figure A around a point will align it with Figure B. You need to find the angle of rotation and the center of rotation.

4. Reflection: Check if reflecting Figure A across a line (like the x-axis, y-axis, or a diagonal) can create Figure B.

5. Dilation: If the size of Figure A needs to change to match Figure B, determine if a scaling transformation (dilation) is appropriate.

6. Combining Transformations: Sometimes, multiple transformations are needed in a sequence to achieve the exact mapping.

To provide the correct transformation sequence, I would need more details about the shapes. If you can describe the figures or provide their coordinates, I can help you determine the exact sequence of transformations needed.

Answer 4

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Part 1 of 2
(a) Which sequence(s) of transformations will map Figure A onto Figure B exactly

Translate Figure A to the left units, and then dilate that result with scale factor centered at the origin.

Dilate Figure A with scale factor centered at the origin, and then translate that result to the left units.

Dilate Figure A with scale factor centered at the origin, and then reflect that result over the -axis.

Dilate Figure A with scale factor centered at the origin, and then rotate that result clockwise about the origin.

None of these

Answer 5

To determine which sequence of transformations would correctly map Figure A onto Figure B, we need to consider the effects of the transformations proposed in each option:

1. Translate Figure A to the left and then dilate:

   • This will first move Figure A to the left on the coordinate plane, and then enlarge it based on the specified center. This might change the overall positioning and size but does not revert any transformations done to the figure itself.

2. Dilate Figure A and then translate:

   • This dilates the figure first, changing its size while retaining its center, and then shifts the larger figure left. This also will alter the relationship of the figure’s size to its position.

3. Dilate Figure A and then reflect over the x-axis:

   • This will enlarge the figure first and then reflect it across the x-axis. This could be useful if Figure B is a mirror image of Figure A, but would not be appropriate if positions differ only by translation or scaling without reflection.

4. Dilate Figure A and then rotate clockwise about the origin:

   • This enlarges the figure first and then rotates it, which can be effective if Figure B is a rotated version of Figure A after enlargement.

5. None of these:

   • This option suggests that none of the provided sequences correctly map Figure A onto Figure B.

Conclusion:

Without visual information regarding the arrangement and orientation of Figures A and B, I can't definitively select the correct transformation sequence. However, if you know the relationship between the figures (e.g., is one a mirror image, rotated version, etc.), that information could help make a more confident choice.

If you can describe the differences between Figure A and Figure B (such as their positions, relative orientations, etc.), I would be glad to assist further in choosing the correct transformation sequence!