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The problem states that the coordinates of the endpoints of line segment \( GH \) are \( G(2, 7) \) and \( H(11, 16) \), and point \( I \) divides the line segment such that the ratio of \( GI:HI \) is 4:5.

To find the coordinates of point \( I \), we can use the section formula. When a point divides a line segment in a given ratio, the formula for finding the coordinates of the dividing point is:

\[
I(x, y) = \left( \frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n} \right)
\]

Here:
- \( G(x_1, y_1) = (2, 7) \)
- \( H(x_2, y_2) = (11, 16) \)
- The ratio \( GI:HI = 4:5 \), so \( m = 4 \) and \( n = 5 \).

Substitute these values into the formula:

\[
I(x, y) = \left( \frac{4 \cdot 11 + 5 \cdot 2}{4+5}, \frac{4 \cdot 16 + 5 \cdot 7}{4+5} \right)
\]

Let's calculate the coordinates of point \( I \).The coordinates of point \( I \), which divides line segment \( GH \) in the ratio 4:5, are \( I(6, 11) \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the section formula change if the ratio were 5:4 instead?
2. Can we use the same method to divide a 3D line segment into a given ratio?
3. How can you verify that point \( I \) indeed divides the segment in the 4:5 ratio?
4. How would the midpoint of the line segment \( GH \) be calculated?
5. If the ratio were \( GI:HI = k:1 \), how would the formula adapt?

**Tip:** The section formula is powerful for dividing line segments in both internal and external ratios.

The coordinates of the endpoints of GH are G(2, 7) and H(11, 16). Point I is on GH and divides it such that GI:HI is 4:5.

Learn how to find the coordinates of a point that divides the line segment GH, with endpoints G(2,7) and H(11,16), in the ratio GI:HI = 4:5 using the section formula. Suitable for students in Grades 8-10.

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