How do you enlarge the pentagon and its interior segments by a scale factor of 2. Then, enlarge it again by a scale factor of 4?
enlarge it just once with a scale factor of 8
To enlarge a polygon and its interior segments, you need to multiply the coordinates of the vertices by the desired scale factor.
Let's say you have a pentagon with vertices A, B, C, D, and E. To enlarge it by a scale factor of 2, you would follow these steps:
1. Calculate the coordinates of the midpoints of the line segments connecting the vertices of the pentagon. Let's call them F, G, H, I, and J. These midpoints can be calculated by averaging the coordinates of the endpoints of each line segment.
2. Multiply the x and y coordinates of each vertex and midpoint by the scale factor of 2.
- For each point P(x, y):
- New x-coordinate = 2 * x
- New y-coordinate = 2 * y
3. Connect the new vertices and midpoints to form a new enlarged pentagon.
To enlarge it further by a scale factor of 4, simply repeat steps 1-3 using the enlarged pentagon from the previous step. Instead of multiplying by 2, you would multiply by 4 when calculating the new coordinates.
It's important to note that the scale factor determines the proportionate increase in size. Enlarging a figure by a scale factor of 2 makes it twice as large, and enlarging it by a scale factor of 4 makes it four times as large.