To find the possible coordinates of the midpoint of segment AR, you can use the midpoint formula, which calculates the midpoint (M) of a line segment with two endpoints A and R:
Midpoint (M) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
In this case, you're given the coordinates of point A (0, 0) and point R (5, y), where y is the y-coordinate of point R.
So, the midpoint coordinates (M) would be:
M = [(0 + 5) / 2, (0 + y) / 2]
M = [5/2, y/2]
Now, you have the x-coordinate of the midpoint (5/2) and a variable for the y-coordinate (y/2).
For segment AT, you can use the same midpoint formula with coordinates A (0, 0) and T (x, 7):
M = [(0 + x) / 2, (0 + 7) / 2]
M = [x/2, 7/2]
Now, you have the x-coordinate (x/2) and the y-coordinate (7/2) of the midpoint for segment AT.
For segment RT, you can use the coordinates of points R (5, y) and T (x, 7):
M = [(5 + x) / 2, (y + 7) / 2]
M = [(5 + x) / 2, (y + 7) / 2]
Now, you have the x-coordinate [(5 + x) / 2] and the y-coordinate [(y + 7) / 2] of the midpoint for segment RT.
So, the possible coordinates of the midpoint depend on the values of x and y, which may vary depending on the specific values you have for those coordinates.