Find the coordinates of the point three tenths
 of the way from A to B. a is (-4,-6)  B is (11,4)

To find the coordinates of a point that is a certain fraction of the way from point \( A(x_1, y_1) \) to point \( B(x_2, y_2) \), we can use the section formula. 

Given:

- Point \( A(-4, -6) \)
- Point \( B(11, 4) \)
- The point is three-tenths of the way from \( A \) to \( B \)

We use the formula for the point dividing the line segment in the ratio \( m:n \):

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

Here, \( m = 3 \) (the portion of the way), and \( n = 7 \) (the remaining part to make the full length).

Now, substituting the values:

\[
P_x = \frac{3 \cdot 11 + 7 \cdot (-4)}{3 + 7} = \frac{33 - 28}{10} = \frac{5}{10} = 0.5
\]
\[
P_y = \frac{3 \cdot 4 + 7 \cdot (-6)}{3 + 7} = \frac{12 - 42}{10} = \frac{-30}{10} = -3
\]

Thus, the coordinates of the point three-tenths of the way from \( A \) to \( B \) are:

\[
P(0.5, -3)
\]

Would you like more details or have any questions?

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Here are 5 related questions for deeper understanding:

1. How do you calculate the midpoint of a line segment between two points?
2. Can you find the coordinates of the point two-thirds of the way from \( A \) to \( B \)?
3. How would the coordinates change if the point were seven-tenths of the way from \( A \) to \( B \)?
4. How does the section formula apply to 3D coordinates?
5. What is the geometric meaning of dividing a line segment in a certain ratio?

**Tip:** The section formula can also be used to divide a segment externally, not just internally, depending on the ratio!

Find the coordinates of the point three-tenths of the way from A to B. A is (-4,-6) B is (11,4)

Learn how to find the coordinates of a point three-tenths of the way from point A (-4, -6) to point B (11, 4). This solution uses the section formula to divide the line segment into a ratio and is suitable for students in Grades 9-11. Explore key concepts in coordinate geometry and ratios.

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