Final answer:
To find point G with M as the midpoint of GH and H's coordinates given, solve the midpoint formula equations to get G's coordinates, which are (2, 2).
Step-by-step explanation:
The task here is to find the coordinates of point G, given that M is the midpoint of the segment GH and has coordinates M(1, 4). We also know that point H is at (0, 6). To find point G, we can use the midpoint formula which states that the midpoint M's coordinates are the average of the x-coordinates and the y-coordinates of G and H, respectively.
Since M is the midpoint, the equations will be:
1 = (xG + 0)/2
4 = (yG + 6)/2
Solving these equations for G's coordinates, we get:
xG = 2(1) - 0 = 2
yG = 2(4) - 6 = 2
So the coordinates of point G are (2, 2).