Question

se a coordinate proof to show that triangle ABC is scalene. What are the lengths of sides AB , BC , and AC ?(1 point)ResponsesAB≈10.6, BC≈8.1, and AC≈7.1; therefore, ABC is a scalene triangle.    cap A cap b almost equal to 10 point 6 , cap b cap c almost equal to 8 point 1 , and cap A cap c almost equal to 7 point 1 ; therefore,  upper A upper B upper C is a scalene triangle.AB≈3.6, BC≈6.1, and AC≈4.2; therefore, ABC is a scalene triangle.cap A cap b almost equal to 3 point 6 , cap b cap c almost equal to 6 point 1 , and cap A cap c almost equal to 4 point 2 ; therefore,  upper A upper B upper C is a scalene triangle.AB≈10.6, BC≈6.4, and AC≈7.1; therefore, ABC is a scalene triangle.  cap A cap b almost equal to 10 point 6 , cap b cap c almost equal to 6 point 4 , and cap A cap c almost equal to 7 point 1 ; therefore,  upper A upper B upper C is a scalene triangle.AB≈8.5, BC≈6.4, and AC≈7.1; therefore, ABC is a scalene triangle.

Answer 1

To show that triangle ABC is scalene using coordinate proof, we need to demonstrate that all three sides (AB, BC, and AC) have different lengths.

Let's analyze the given responses and calculate the approximate lengths for each triangle:

1. **First option:**
- AB ≈ 10.6
- BC ≈ 8.1
- AC ≈ 7.1
- All sides have different lengths, so triangle ABC is scalene.

2. **Second option:**
- AB ≈ 3.6
- BC ≈ 6.1
- AC ≈ 4.2
- All sides have different lengths, so triangle ABC is scalene.

3. **Third option:**
- AB ≈ 10.6
- BC ≈ 6.4
- AC ≈ 7.1
- All sides have different lengths, so triangle ABC is scalene.

4. **Fourth option:**
- AB ≈ 8.5
- BC ≈ 6.4
- AC ≈ 7.1
- All sides have different lengths, so triangle ABC is scalene.

All four provided options result in triangle ABC being scalene since all side lengths are distinct in each case. Therefore, any of the responses you provided would validly show that triangle ABC is scalene, based on the distinct lengths of its sides.