Final answer:
To find the missing coordinate of the square with given points (0, 4), (8, 4), and (8, 12), we identify the side length as 8. We use this information along with the horizontal and vertical alignment of known points to deduce the missing coordinate is (0, 12).
Step-by-step explanation:
The question asks to find the missing coordinate of a square given three of its coordinates. The known coordinates are (0, 4), (8, 4), and (8, 12). Because these points show a square, we can deduce that it has equal sides and right angles at each corner.
To find the fourth coordinate, we notice that the y-coordinate for the first two points is the same, meaning they form a horizontal line. Thus, these two points are on the same side of the square. The difference in x-coordinates (8 - 0) tells us that the side length of the square is 8.
Now, we look at the third coordinate, (8, 12). The x-coordinate matches with the second point, so this is a vertical side. The difference in y-coordinates (12 - 4) is also 8, reaffirming the side length. Hence, if we subtract 8 from the x-coordinate of the third point, keeping the y-coordinate the same (since we are moving horizontally to the left to close the square), we get the fourth point which is (0, 12).