https://file.aiquickdraw.com/mathbot/file/1727369744542raudio5z.jpg

The given problem is asking how many distinct planes can be passed through points \( A \), \( B \), and \( C \), given that the distances between them are \( AB = 2 \, \text{cm} \), \( BC = 3 \, \text{cm} \), and \( AC = 5 \, \text{cm} \).

This scenario describes a triangle with the given side lengths, \( AB = 2 \, \text{cm} \), \( BC = 3 \, \text{cm} \), and \( AC = 5 \, \text{cm} \). To determine how many distinct planes can pass through these points, we need to check if the points are collinear.

### Step 1: Verify if the points are collinear
If points \( A \), \( B \), and \( C \) are collinear, they lie on the same straight line, and therefore only **one plane** can be passed through these points.

Using the triangle inequality theorem:

- \( AB + BC = 2 + 3 = 5 = AC \)

Since the sum of the lengths of \( AB \) and \( BC \) is exactly equal to \( AC \), the points are collinear. Therefore, the three points lie on the same line.

### Conclusion:
Only **one distinct plane** can be passed through points \( A \), \( B \), and \( C \), since they are collinear.

---

Do you want more details on the triangle inequality theorem or collinearity? 

Here are 5 related questions:
1. How does the triangle inequality theorem determine if points are collinear?
2. What are the conditions for three points to lie in the same plane?
3. Can three points in space ever define more than one plane?
4. What if the points were not collinear — how many planes could pass through them?
5. How would the problem change if one of the distances was different?

**Tip:** To determine collinearity, check if the sum of two side lengths equals the third side in a triangle.

Скільки РІЗНИХ площин можна провести через точки A, B і C, якщо AB=2см, BC=3см, AC=5см?

Learn how to determine the number of distinct planes that can pass through points A, B, and C with distances AB=2cm, BC=3cm, and AC=5cm. Explore the concept of collinearity using the triangle inequality theorem. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation