Determining the scale factor on a graph involves comparing the dimensions of a figure and its scaled version. Here's a breakdown of how to do it:
1. Identify Corresponding Sides:
- Locate corresponding sides on both the original figure and the scaled figure. Corresponding sides are sides that occupy the same relative position in both figures.
2. Measure the Lengths:
- Carefully measure the lengths of the corresponding sides. Ensure you're using the same units for both measurements.
3. Calculate the Scale Factor:
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The scale factor is the ratio of the length of a side on the new (scaled) figure to the length of the corresponding side on the original figure.
- Scale Factor = (Length of side on the new figure) / (Length of side on the original figure)
4. Interpret the Scale Factor:
- Scale Factor > 1: The figure has been enlarged (scaled up). For example, a scale factor of 2 means the new figure is twice as big as the original.
- Scale Factor < 1: The figure has been reduced (scaled down). For example, a scale factor of 0.5 (or 1/2) means the new figure is half the size of the original.
- Scale Factor = 1: The figure is the same size.
Example:
Let's say you have a square on a graph. The original square has sides of length 2 units. The scaled square has sides of length 6 units.
- Scale Factor = (Length of side on the new square) / (Length of side on the original square)
- Scale Factor = 6 / 2
- Scale Factor = 3
This means the square has been enlarged by a scale factor of 3.
Another Example (Reduction):
Original triangle side length: 8 units
Scaled triangle side length: 4 units
- Scale Factor = 4/8
- Scale Factor = 1/2 or 0.5
This means the triangle has been reduced to half its original size.
Important Considerations:
- Consistency: The scale factor should be the same for all corresponding sides. If it isn't, the figures are not similar.
- Graphs and Coordinates: When working with coordinates on a graph, you can determine the side lengths by calculating the distance between the coordinates (e.g., using the distance formula or simply counting units if the sides are horizontal or vertical).
In summary, to find the scale factor on a graph, measure corresponding sides of the original and scaled figures and then divide the length of the side on the scaled figure by the length of the side on the original figure.
