Final answer:
The coordinates of the point 7/10 of the way from point A (-4, -6) to point B (11, 7) are found by vector scaling and addition, resulting in the point (6.5, 3.1).
Step-by-step explanation:
To find the coordinates of a point that lies 7/10 of the way from A to B, we need to use the concept of vector scaling and vector addition. Suppose points A (-4,-6) and B (11,7) are in a Cartesian coordinate system. The process involves calculating the vector from A to B, scaling this vector by 7/10, and then adding this scaled vector to point A to find the required point.
The vector from A to B is found by subtracting the coordinates of A from B:
Vector AB = (11 - (-4), 7 - (-6)) = (15, 13)
We then scale this vector by 7/10:
Scaled vector = (15 * 7/10, 13 * 7/10) = (10.5, 9.1)
The coordinates of the desired point can now be found by adding this scaled vector to point A:
Point P = (-4 + 10.5, -6 + 9.1) = (6.5, 3.1)
Therefore, the coordinates of the point that lies 7/10 of the way from A to B are (6.5, 3.1).