Question
Find the scale factor.
Two triangles on a coordinate plane
Answers
GPT-4o mini
To find the scale factor between two triangles on a coordinate plane, you need the lengths of corresponding sides of the triangles. The scale factor is the ratio of the lengths of corresponding sides between the two triangles.
Here’s how you can do it step by step:
1. **Identify the Corresponding Vertices**: Label the vertices of the first triangle as \(A\), \(B\), and \(C\) and the vertices of the second triangle as \(A'\), \(B'\), and \(C'\).
2. **Calculate the Lengths of Corresponding Sides**:
- Use the distance formula to calculate the lengths of the sides of both triangles. The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
- Calculate the lengths for sides \(AB\) and \(A'B'\), \(BC\) and \(B'C'\), and \(CA\) and \(C'A'\).
3. **Calculate the Scale Factor**:
- The scale factor can be found by taking the ratio of one pair of corresponding sides. For example:
\[
\text{Scale Factor} = \frac{\text{length of side in triangle 2}}{\text{length of corresponding side in triangle 1}}
\]
- Ensure to check that the ratio remains consistent across all corresponding sides.
4. **Result**: If the ratios of all corresponding sides are the same, that value is the scale factor.
If you provide the coordinates of the vertices of both triangles, I can help you find the scale factor explicitly.
Here’s how you can do it step by step:
1. **Identify the Corresponding Vertices**: Label the vertices of the first triangle as \(A\), \(B\), and \(C\) and the vertices of the second triangle as \(A'\), \(B'\), and \(C'\).
2. **Calculate the Lengths of Corresponding Sides**:
- Use the distance formula to calculate the lengths of the sides of both triangles. The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
- Calculate the lengths for sides \(AB\) and \(A'B'\), \(BC\) and \(B'C'\), and \(CA\) and \(C'A'\).
3. **Calculate the Scale Factor**:
- The scale factor can be found by taking the ratio of one pair of corresponding sides. For example:
\[
\text{Scale Factor} = \frac{\text{length of side in triangle 2}}{\text{length of corresponding side in triangle 1}}
\]
- Ensure to check that the ratio remains consistent across all corresponding sides.
4. **Result**: If the ratios of all corresponding sides are the same, that value is the scale factor.
If you provide the coordinates of the vertices of both triangles, I can help you find the scale factor explicitly.