To find the missing coordinate for this square, we need to examine the given coordinates and determine the position of the fourth vertex.

Given Coordinates:

1. $(5, -4)$
2. $(10, -4)$
3. $(10, 1)$

Since it is a square, the sides are parallel to the coordinate axes, meaning the missing coordinate should complete a square pattern.

Steps:

1. Observe that two points, $(5, -4)$ and $(10, -4)$, share the same $y$-coordinate, which suggests they lie on a horizontal line.
2. Similarly, the points $(10, -4)$ and $(10, 1)$ share the same $x$-coordinate, indicating they are aligned vertically.

Deduction of the Missing Point:

• The point $(5, -4)$ is horizontally aligned with $(10, -4)$.
• To complete the square, we need a point that is vertically aligned with $(5, -4)$ and horizontally aligned with $(10, 1)$.

Therefore, the missing point is $(5, 1)$.

Answer:

The missing coordinate is $(5, 1)$.

Would you like a further breakdown or have any questions?

Here are some related questions to explore further:

1. How do we determine if four points form a square?
2. How can we generalize this method to find missing vertices for other quadrilaterals?
3. What properties do squares and rectangles share when plotted on a coordinate plane?
4. How would this method change if the sides of the square were not parallel to the coordinate axes?
5. Can we determine the area of the square from these coordinates?

Tip: When dealing with squares or rectangles on a coordinate plane, remember that opposite sides are both parallel and equal in length.