https://file.aiquickdraw.com/mathbot/file/1727303976156kk36rimz.jpg

To find the coordinates of the point that is \(\frac{7}{10}\) of the way from point A to point B, we use the section formula. The formula for finding a point that divides a line segment in a given ratio is:

\[
(x, y) = \left( x_1 + \frac{r}{r+s}(x_2 - x_1), y_1 + \frac{r}{r+s}(y_2 - y_1) \right)
\]

Where:
- \( A(x_1, y_1) \) and \( B(x_2, y_2) \) are the coordinates of points A and B,
- \( r \) is the fraction (in this case, 7) of the distance to the point,
- \( r+s = 10 \), so the total distance is divided in the ratio \( \frac{7}{10} \).

From the graph:
- Point A has coordinates \( A(-4, -8) \),
- Point B has coordinates \( B(10, 6) \).

Now, I'll plug these values into the formula. Let me calculate it for you.The coordinates of the point that is \(\frac{7}{10}\) of the way from point A \((-4, -8)\) to point B \((10, 6)\) are approximately \((5.8, 1.8)\).

Would you like more details or have any further questions?

Here are some related questions to explore:
1. How does the section formula change for different ratios?
2. What if the point is halfway between A and B? How would the coordinates change?
3. Can you apply the section formula to three-dimensional points?
4. What happens when the fraction is negative in the section formula?
5. How can you find the midpoint between two points?

**Tip:** For any fraction \( \frac{p}{q} \) along a line, the formula scales the distances proportionally to \( p \) and \( q \).

Find the coordinates of the point 7/10 of the way from A(-4, -8) to B(10, 6).

Learn how to find the coordinates of the point that is 7/10 of the way from point A (-4, -8) to point B (10, 6) using the section formula in coordinate geometry. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation