Dilate the figure with a scale factor of 1/3 and the center at (4,3). Give the points?
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It says Dilate the figure with scale factor of 1/3 and the center at (4.3). Give the points below. Show work for credit.
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To dilate a figure with a scale factor of 1/3 and a center at (4,3), you can follow this process:
1. Start with the original figure.
2. Calculate the distance from each point of the original figure to the center point (4,3).
3. Multiply the calculated distance by the scale factor of 1/3.
4. Use the new distance to find the corresponding point of the dilated figure.
Let's assume you have a specific figure with its points defined. For example, let's say we have point A at (1, 2), point B at (3, 4), and point C at (5, 6).
1. Start with the original figure:
- Point A: (1, 2)
- Point B: (3, 4)
- Point C: (5, 6)
2. Calculate the distance from each point to the center point (4,3):
- Distance from A to center = sqrt((4-1)^2 + (3-2)^2) = sqrt(9+1) = sqrt(10)
- Distance from B to center = sqrt((4-3)^2 + (3-4)^2) = sqrt(1+1) = sqrt(2)
- Distance from C to center = sqrt((4-5)^2 + (3-6)^2) = sqrt(1+9) = sqrt(10)
3. Multiply the calculated distance by the scale factor of 1/3:
- Dilated distance from A to center = (1/3) * sqrt(10)
- Dilated distance from B to center = (1/3) * sqrt(2)
- Dilated distance from C to center = (1/3) * sqrt(10)
4. Use the new distance to find the corresponding point of the dilated figure by adding the dilated distance to the center's x and y coordinates:
- Dilated point A: (4 + (1/3) * sqrt(10), 3 + (1/3) * sqrt(10))
- Dilated point B: (4 + (1/3) * sqrt(2), 3 + (1/3) * sqrt(2))
- Dilated point C: (4 - (1/3) * sqrt(10), 3 - (1/3) * sqrt(10))
So, the points of the dilated figure with a scale factor of 1/3 and a center at (4,3) are:
- Dilated point A: (4 + (1/3) * sqrt(10), 3 + (1/3) * sqrt(10))
- Dilated point B: (4 + (1/3) * sqrt(2), 3 + (1/3) * sqrt(2))
- Dilated point C: (4 - (1/3) * sqrt(10), 3 - (1/3) * sqrt(10))