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To find the coordinates of point \( K \) on the line segment \( JL \) such that \( JK \) is \( \frac{3}{7} \) of \( JL \), we can use the section formula for dividing a line segment internally.

The section formula gives the coordinates of a point \( K(x, y) \) dividing the line segment joining points \( J(x_1, y_1) \) and \( L(x_2, y_2) \) in the ratio \( m:n \) as:

\[
K(x, y) = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)
\]

Here:
- \( J = (-18, -17) \)
- \( L = (3, 11) \)
- The ratio \( m:n = 3:4 \) (since \( JK = \frac{3}{7} \) of \( JL \), so \( JL = 3+4 = 7 \))

Let's calculate the coordinates of \( K \).The coordinates of point \( K \) are \( (-9, -5) \).

Would you like further details or have any other questions?

Here are some related questions:
1. How does the section formula work in 3D space?
2. What happens if the ratio \( JK/JL \) is changed?
3. Can you explain how the midpoint formula is derived from the section formula?
4. How do we find the coordinates of a point dividing a line segment externally?
5. How would the process change if we needed the distance from \( J \) to \( K \) instead of the coordinates?

**Tip:** The section formula is very versatile and can be applied for both internal and external division of a segment!

The point K lies on the segment JL. Find the coordinates of K so that JK is 3/7 of JL.

Learn how to calculate the coordinates of point K that lies on the segment JL where JK is 3/7 of JL. This involves using the section formula, making it a suitable problem for students in Grades 9-11. The points J(-18, -17) and L(3, 11) are provided to help determine the coordinates of K.

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