Point O lies on 
MN
 such that MO:NO is 1:5. Graph O.

To graph the point \( O \) on line segment \( MN \) where the ratio \( MO:NO = 1:5 \), we can follow these steps:

1. **Determine coordinates of \( M \) and \( N \)**:
   Let the coordinates of point \( M \) be \( M(x_1, y_1) \) and point \( N \) be \( N(x_2, y_2) \).

2. **Find the coordinates of point \( O \)**:
   The point \( O \) divides the line segment in the ratio 1:5. Using the section formula, the coordinates of point \( O(x, y) \) can be calculated as:
   \[
   x = \frac{m x_2 + n x_1}{m + n}
   \]
   \[
   y = \frac{m y_2 + n y_1}{m + n}
   \]
   where \( m:n = 1:5 \), \( x_1, y_1 \) are the coordinates of \( M \), and \( x_2, y_2 \) are the coordinates of \( N \).

3. **Substitute the values into the formula**:
   Plug in the given ratio and the coordinates of points \( M \) and \( N \) to get the exact position of point \( O \).

If you provide the coordinates of \( M \) and \( N \), I can compute the exact coordinates of point \( O \) and help you graph it.

Would you like me to explain the formula in more detail or continue with another step? 

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Here are five relative questions you might want to explore:
1. What is the section formula used in other ratios?
2. How can we use the midpoint formula to verify results?
3. How does the ratio \( m:n \) affect the placement of point \( O \)?
4. What is the geometric significance of dividing a line segment in a given ratio?
5. Can you calculate the distance between \( M \) and \( O \)?

**Tip**: The section formula is useful for dividing line segments in any ratio, and can be used to solve a variety of geometric problems.

Point O lies on MN such that MO:NO is 1:5. Graph O.

Explore how to graph point O on line segment MN where the ratio of MO to NO is 1:5. Learn how to apply the section formula to find the exact coordinates of O using the coordinates of points M and N. This problem focuses on coordinate geometry and ratio concepts, suitable for students in Grades 8-10.

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