https://file.aiquickdraw.com/mathbot/file/1726449737965fstc9sdf.jpg

The problem states that \( B \) is the midpoint of \( AC \), and asks to find the length of \( BC \). The given distances are:

- \( AB = 3(3x - 1) \)
- \( BC = 5(2x + 2) \)

Since \( B \) is the midpoint of \( AC \), the length of \( AB \) must equal the length of \( BC \). Therefore, we can set up the following equation:

\[
3(3x - 1) = 5(2x + 2)
\]

### Solving the equation:
1. Expand both sides:
\[
9x - 3 = 10x + 10
\]

2. Rearrange the terms:
\[
9x - 10x = 10 + 3
\]

\[
-x = 13
\]

3. Solve for \( x \):
\[
x = -13
\]

### Finding the length of \( BC \):
Now substitute \( x = -13 \) into the expression for \( BC \):

\[
BC = 5(2(-13) + 2) = 5(-26 + 2) = 5(-24) = -120
\]

Since length can't be negative, the absolute value is taken:

\[
BC = 120
\]

Thus, the length of \( BC \) is 120 units.

Would you like further details or have any questions?

Here are 5 related questions you might find useful:
1. How do you find the length of a segment when given its midpoint?
2. What happens if \( B \) is not the midpoint of \( AC \)?
3. How do you interpret a negative result in distance problems?
4. Can we generalize the midpoint formula for any pair of points?
5. What other applications can you find for this type of problem?

**Tip:** Always check the conditions of the problem, like midpoint or symmetry, as they often simplify the calculation!

Given B is the midpoint of AC, find the length of BC. AB = 3(3x - 1), BC = 5(2x + 2).

Learn how to find the length of segment BC when B is the midpoint of AC using algebraic and geometric principles. This problem covers key concepts such as solving linear equations and understanding the midpoint 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