Final answer:
The coordinates of the point that is two-fifths of the distance from (-2, 1) to (8, 11) are (2, 5).
Step-by-step explanation:
To find the coordinates of the point that is two-fifths of the distance from (-2, 1) to (8, 11), we must first find the vector from the first point to the second one and then multiply it by ⅓ (2/5). The vector from (-2, 1) to (8, 11) is obtained by subtracting the coordinates of the first point from the second point's coordinates, giving us the vector (8 - (-2), 11 - 1) = (10, 10). To find two-fifths of this vector, we multiply each component by 2/5, yielding (10 × 2/5, 10 × 2/5) = (4, 4). Finally, to find the actual coordinates of the required point, we add this vector to the coordinates of the first point (-2, 1). Therefore, the new point's coordinates are (-2 + 4, 1 + 4) = (2, 5).