Final answer:
To find the fourth corner of a square given the other three corners, we observe the changes in x and y values between the known points and apply these changes to find the missing point. The coordinates of the fourth corner of the square are (9, 3).
Step-by-step explanation:
The task is to find the coordinates of the fourth corner of a square given three corners.
To do this, we need to use the properties of a square to determine the missing point. Squares have sides of equal length and right angles between the sides.
The corners of the square provided are (1, 7), (5, 3), and (9, 7). We can see that moving from the first point (1, 7) to the second point (5, 3), the change in x is +4 (5-1) and the change in y is -4 (3-7), which suggests a movement diagonally across the square.
Since two sides of the square have already been determined by these corners, the fourth corner must preserve the same differences in x and y values.
In moving from (9, 7) to the unknown corner, we need to reverse the change in y that occurred between (1, 7) and (5, 3) while maintaining the change in x because the fourth point also forms a diagonal with (5, 3).
Therefore, starting from (9, 7), we subtract 4 from the y-coordinate and keep the x-coordinate the same, giving us the fourth point as (9, 3).
So, the coordinates of the fourth corner of the square are (9, 3).