Question
When you have two shapes to compare on a coordinate plane, you can determine the scale factor, knowing that the transformation was a dilation. Generate instructions you would give another student to determine the scale factor. make the writing short
Answers
GPT-4o mini
To determine the scale factor between two shapes on a coordinate plane after a dilation, follow these steps:
1. **Identify Corresponding Points**: Choose a pair of corresponding points (e.g., A and A') from the original shape and its dilated image.
2. **Calculate Distances**: Find the distance from the center of dilation (point O) to the original point (A) and to the dilated point (A').
- Use the distance formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
3. **Determine Scale Factor**: Divide the distance to the dilated point by the distance to the original point:
\[
\text{Scale Factor} = \frac{\text{Distance from O to A'}}{\text{Distance from O to A}}
\]
4. **Repeat**: Check with another pair of corresponding points (e.g., B and B') to ensure consistency in the scale factor.
5. **Conclude**: The scale factor remains the same for all corresponding points if the transformation is a uniform dilation.
That's it! You've determined the scale factor.
1. **Identify Corresponding Points**: Choose a pair of corresponding points (e.g., A and A') from the original shape and its dilated image.
2. **Calculate Distances**: Find the distance from the center of dilation (point O) to the original point (A) and to the dilated point (A').
- Use the distance formula: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
3. **Determine Scale Factor**: Divide the distance to the dilated point by the distance to the original point:
\[
\text{Scale Factor} = \frac{\text{Distance from O to A'}}{\text{Distance from O to A}}
\]
4. **Repeat**: Check with another pair of corresponding points (e.g., B and B') to ensure consistency in the scale factor.
5. **Conclude**: The scale factor remains the same for all corresponding points if the transformation is a uniform dilation.
That's it! You've determined the scale factor.