Final answer:
To find point B on line segment AC with a ratio of AB to AC of 1:3, apply the section formula to get the coordinates B=(-0.5, 4.75).
Step-by-step explanation:
Point B on line segment AC can be found using the section formula. Since the ratio of AB to AC is 1:3, this implies that B divides AC in the ratio of 1:3. To find the coordinates of B, we can use the ratio to partition the horizontal (x-coordinate) and vertical (y-coordinate) distances between A and C.
The x-coordinate of B is computed as follows: x_B = (1*4 + 3*(-2)) / (1+3) = (4 - 6) / 4 = -0.5. Similarly, the y-coordinate of B is computed as: y_B = (1*7 + 3*4) / (1+3) = (7 + 12) / 4 = 4.75. Therefore, the coordinates of point B are B=(-0.5, 4.75).