Find the distance of segment MN, given: M(5, 10 ) and N(-3, 10 )

Given: B lies between A and C. AB = x + 1, BC = 2x+ 3, and AC = 31 
Draw an example of the problem ( 2 pts), and then Solve for X (2 pts)

Let's break down the two parts of your question.

### Part 1: Finding the Distance of Segment MN
You are given points \( M(5, 10) \) and \( N(-3, 10) \). The distance between two points \( M(x_1, y_1) \) and \( N(x_2, y_2) \) can be calculated using the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the given coordinates:

\[
d = \sqrt{((-3 - 5)^2 + (10 - 10)^2)} = \sqrt{(-8)^2 + (0)^2} = \sqrt{64} = 8
\]

Thus, the distance of segment MN is **8 units**.

---

### Part 2: Solving for \( x \) in the Segment Addition Problem

You are given that point \( B \) lies between points \( A \) and \( C \), and:

- \( AB = x + 1 \)
- \( BC = 2x + 3 \)
- \( AC = 31 \)

Since \( AC = AB + BC \) by the segment addition postulate, we can write the equation:

\[
(x + 1) + (2x + 3) = 31
\]

Now solve for \( x \):

\[
x + 1 + 2x + 3 = 31
\]
\[
3x + 4 = 31
\]
\[
3x = 31 - 4
\]
\[
3x = 27
\]
\[
x = \frac{27}{3} = 9
\]

Thus, the value of \( x \) is **9**.

---

### Example Drawing of the Problem:

- Draw three points in a line labeled \( A \), \( B \), and \( C \) with \( B \) between \( A \) and \( C \).
- Indicate that \( AB = x + 1 \), \( BC = 2x + 3 \), and \( AC = 31 \).

---

Would you like me to generate a visual representation of this problem?

### Related Questions:
1. How do you apply the distance formula for points in 3D space?
2. What happens if the coordinates of \( M \) and \( N \) had different \( y \)-coordinates?
3. Can the value of \( x \) be negative in the segment addition problem?
4. How would you solve for \( x \) if different equations for \( AB \) and \( BC \) were given?
5. How is the segment addition postulate useful in geometric proofs?

### Tip:
Always double-check your algebraic manipulations when solving for unknowns in geometry.

Find the distance of segment MN, given: M(5, 10 ) and N(-3, 10 ). Given: B lies between A and C. AB = x + 1, BC = 2x+ 3, and AC = 31. Draw an example of the problem (2 pts), and then Solve for X (2 pts).

Learn how to find the distance between points M(5, 10) and N(-3, 10) using the distance formula, and solve for X in a segment addition problem where AB = x + 1, BC = 2x + 3, and AC = 31. This step-by-step solution is suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation