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The question in the image appears to involve finding the coordinate of point \( K \) between points \( J \) and \( L \), with a given ratio of distances.

Here’s a step-by-step approach to solving this type of problem:

### Problem:
You are given that \( K \) lies between points \( J \) and \( L \), and the ratio of the distances from \( J \) to \( K \) and from \( K \) to \( L \) is 2:3. The goal is to find the coordinate of point \( K \), given that the positions of \( J \) and \( L \) are specified on a number line.

### Solution Outline:
1. Let the coordinates of \( J \) and \( L \) be \( x_J \) and \( x_L \), respectively.
2. The point \( K \) divides the line segment between \( J \) and \( L \) in the ratio 2:3.
3. Use the section formula for internal division, which states that if a point \( K \) divides a segment joining two points \( A(x_A) \) and \( B(x_B) \) in the ratio \( m:n \), then the coordinate of \( K \) is:
   \[
   x_K = \frac{m \cdot x_B + n \cdot x_A}{m + n}
   \]
4. In this case, the ratio is 2:3, so the coordinate of \( K \) can be computed using this formula.

Would you like me to walk you through this with specific coordinates for \( J \) and \( L \), or do you have more details on their values? Let me know if you'd like further clarification or if you'd like to discuss similar problems!

Here are five related questions that expand upon this:

1. How would you apply the section formula if the ratio was reversed to 3:2?
2. How do you handle cases where the division is external (i.e., when the ratio is negative)?
3. How would you find the midpoint of a segment if no ratio is provided?
4. What happens if the points \( J \) and \( L \) are located on a 3D plane instead of a number line?
5. How can you use the section formula to find points dividing the segment into equal parts?

### Tip:
Always remember that the section formula is versatile and can be applied in various contexts—on number lines, planes, or even in 3D geometry!

In the figure below, K lies between J and L. Find the location of K so that the ratio of JK to KL is 2:3.

Learn how to find the coordinate of point K between J and L on a number line, given the ratio JK:KL is 2:3. The section formula is used to solve this step-by-step. Suitable for Grades 8-10.

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