We are given that ABCD is a square, and the coordinates of points $A$ and $D$ are:

• $A(3, 4)$
• $D(10, 4)$

Since $ABCD$ is a square, the side lengths must all be equal, and the sides are perpendicular to each other.

Step 1: Calculate the side length of the square

The distance between points $A$ and $D$ is along the horizontal (x-axis), so we can calculate the side length using the difference in the x-coordinates of $A$ and $D$:

$\text{Side length} = |10 - 3| = 7$

Step 2: Determine the coordinates of $B$ and $C$

• The side $AB$ is vertical, parallel to the y-axis, so the x-coordinate of point $B$ is the same as point $A$, which is 3.
• Since the side length is 7, we add 7 to the y-coordinate of $A$, which gives us the y-coordinate of point $B$:

$B(3, 4 + 7) = B(3, 11)$

• Similarly, point $C$ is directly to the right of point $B$, so it will have the same y-coordinate as $B$, which is 11.
• The x-coordinate of point $C$ will be the same as point $D$, which is 10.

Thus, the coordinates of point $C$ are:

$C(10, 11)$

Final Answer:

The coordinates of point $C$ are $(10, 11)$.

Would you like more details or further clarification?

Here are 5 related questions:

1. How would you calculate the distance between any two points on a plane?
2. What is the general method to find the coordinates of a point in a square?
3. How can you determine the area of a square using its side length?
4. How would the problem change if the square was rotated?
5. What are the properties of squares and how can they be applied to find unknown points?

Tip: To find coordinates in a square, always check if sides are parallel to the axes. This makes the calculation straightforward!