Points o, a, b lie on the same line. oa = 12 cm, ob = 9 cm. find the distance between the midpoints of segments oa and ob if: a point o lies on the segment ab

To solve this problem, we'll follow these steps:

1. **Define the points on the line:**
   - Let point \( O \) be at position 0 on the number line.
   - Let point \( A \) be at position 12 (since \( OA = 12 \) cm).
   - Let point \( B \) be at position 9 (since \( OB = 9 \) cm).

2. **Find the midpoints of segments \( OA \) and \( OB \):**
   - The midpoint of \( OA \), \( M_1 \), is calculated as:
     \[
     M_1 = \frac{0 + 12}{2} = \frac{12}{2} = 6 \text{ cm}
     \]
   - The midpoint of \( OB \), \( M_2 \), is calculated as:
     \[
     M_2 = \frac{0 + 9}{2} = \frac{9}{2} = 4.5 \text{ cm}
     \]

3. **Find the distance between the midpoints \( M_1 \) and \( M_2 \):**
   \[
   \text{Distance between } M_1 \text{ and } M_2 = |M_1 - M_2| = |6 - 4.5| = 1.5 \text{ cm}
   \]

So, the distance between the midpoints of segments \( OA \) and \( OB \) is **1.5 cm**.

Would you like further details or have any questions?

Here are 5 related questions to explore further:

1. What is the distance between the midpoints if \( OB = 6 \) cm instead of 9 cm?
2. How would the solution change if \( O \) were not on the segment \( AB \)?
3. What if the point \( A \) was at 15 cm and \( B \) at 5 cm, still with \( O \) at 0 cm?
4. How can the problem be generalized if the coordinates are not along a straight line?
5. What is the distance between the midpoints if \( OA \) and \( OB \) were in three-dimensional space?

**Tip:** In coordinate geometry, the midpoint formula can be used to easily find the center point between two coordinates on any axis.

Learn how to calculate the distance between the midpoints of segments OA and OB using coordinate geometry. Understand the midpoint formula and distance formula with a detailed step-by-step solution. Suitable for 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