a hat on a grid has coordinates of (0,4), (0,1), (6,1), (4, 2), (4,4), (3,5), (1,5), and (0,4). What rule would make a hat with line segments twice as long as this hat's(coordinates above) line segments and moved 8 units to the right?
To make a hat with line segments twice as long as the given hat and moved 8 units to the right, you can apply the following rule:
1. Multiply the x-coordinates of each point by 2 to double the length of the line segments.
2. Add 8 to the x-coordinates of each point to move the hat 8 units to the right.
Let's apply this rule to each coordinate point of the given hat:
(0, 4):
- Multiply x-coordinate by 2: 0 * 2 = 0
- Add 8 to the x-coordinate: 0 + 8 = 8
New Coordinate: (8, 4)
(0, 1):
- Multiply x-coordinate by 2: 0 * 2 = 0
- Add 8 to the x-coordinate: 0 + 8 = 8
New Coordinate: (8, 1)
(6, 1):
- Multiply x-coordinate by 2: 6 * 2 = 12
- Add 8 to the x-coordinate: 12 + 8 = 20
New Coordinate: (20, 1)
(4, 2):
- Multiply x-coordinate by 2: 4 * 2 = 8
- Add 8 to the x-coordinate: 8 + 8 = 16
New Coordinate: (16, 2)
(4, 4):
- Multiply x-coordinate by 2: 4 * 2 = 8
- Add 8 to the x-coordinate: 8 + 8 = 16
New Coordinate: (16, 4)
(3, 5):
- Multiply x-coordinate by 2: 3 * 2 = 6
- Add 8 to the x-coordinate: 6 + 8 = 14
New Coordinate: (14, 5)
(1, 5):
- Multiply x-coordinate by 2: 1 * 2 = 2
- Add 8 to the x-coordinate: 2 + 8 = 10
New Coordinate: (10, 5)
(0, 4):
- Multiply x-coordinate by 2: 0 * 2 = 0
- Add 8 to the x-coordinate: 0 + 8 = 8
New Coordinate: (8, 4)
Therefore, the new coordinates for the hat with line segments twice as long and moved 8 units to the right are:
(8, 4), (8, 1), (20, 1), (16, 2), (16, 4), (14, 5), (10, 5), (8, 4).