How do you enlarge a pentagon and it's interior segments by a scale factor of 2. Then, enlarge it again by a scale factor of 4?
To enlarge a pentagon and its interior segments by a scale factor of 2, follow these steps:
1. Draw a pentagon of your choice. Label its vertices as A, B, C, D, and E.
2. Determine the center of enlargement, which is the point from which the figure will be enlarged. Let's call this point O.
3. Select a scale factor of 2. This means that all distances in the enlarged pentagon will be twice as long as the original distances.
4. Measure the distance from point O to each vertex (OA, OB, OC, OD, and OE), and multiply these distances by the scale factor of 2 to get the new distances for the enlarged pentagon.
5. Using a compass, measure the new distances from point O and mark the new vertices for the enlarged pentagon. Connect these vertices to form the new shape. Label these new vertices as A', B', C', D', and E'.
6. Finally, extend the interior segments of the original pentagon from their respective vertices A, B, C, D, and E to their corresponding vertices in the enlarged pentagon A', B', C', D', and E'.
To enlarge the pentagon and its interior segments again by a scale factor of 4, you can repeat the above steps, but with a few modifications:
1. Instead of using the original pentagon, use the enlarged pentagon A', B', C', D', and E' from the previous step.
2. Choose a new center of enlargement, let's say point P.
3. Repeat the above steps, this time considering the scale factor of 4.
4. Measure the distances from point P to each vertex (PA', PB', PC', PD', and PE'), and multiply these distances by the scale factor of 4 to get the new distances for the second enlargement.
5. Use a compass to measure the new distances from point P and mark the new vertices for the second enlarged pentagon. Connect these vertices to form the new shape. Label these new vertices as A", B", C", D", and E".
6. Once again, extend the interior segments of the original pentagon and the first enlargement from their respective vertices A', B', C', D', and E' to their corresponding vertices in the second enlarged pentagon A", B", C", D", and E".
By following these steps, you can successfully enlarge a pentagon and its interior segments by different scale factors.