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The problem asks to find the coordinates of point \( P \) that divides the line segment \( AB \) internally in the ratio 2:1, where:

- Point \( A(3, 7) \)
- Point \( B(4, 8) \)

### Formula for the Section Formula:
If a point \( P(x, y) \) divides a line segment joining points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \), the coordinates of \( P \) are given by:

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

Here, \( m:n = 2:1 \), \( A(3, 7) \), and \( B(4, 8) \).

### Substituting values:
\[
x = \frac{2(4) + 1(3)}{2+1} = \frac{8 + 3}{3} = \frac{11}{3} \approx 3.67
\]
\[
y = \frac{2(8) + 1(7)}{2+1} = \frac{16 + 7}{3} = \frac{23}{3} \approx 7.67
\]

Thus, the coordinates of point \( P \) are approximately \( P(3.67, 7.67) \).

Would you like a more detailed explanation, or do you have any questions?

Here are some related questions to explore:
1. How would the formula change if the ratio were 3:2?
2. What would happen if the point divided the segment externally?
3. How do you calculate the midpoint of a line segment?
4. Can the section formula be used in three dimensions?
5. How is the section formula derived from the concept of weighted averages?

**Tip:** The section formula is helpful in many geometric problems involving line segments and ratios. Understanding it can be useful for higher-dimensional problems as well!

Given the points A(3, 7) and B(4, 8), find the coordinates of the point P that divides AB internally in the ratio 2:1.

Learn how to find the coordinates of a point that divides a line segment joining two points A(3, 7) and B(4, 8) internally in the ratio 2:1 using the section formula. Suitable for students in Grades 9-10.

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