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 $q$.