Let's analyze the information given to determine the coordinates of point $C$.

Given Information:

1. The $x$-coordinate of $C$ is the same as the $x$-coordinate of $A$.
2. The $y$-coordinate of $C$ is greater than the $x$-coordinate of $A$ and less than the $y$-coordinate of $B$.
3. The coordinates of $C$ contain one even and one odd value.

Step-by-Step Solution:

• Coordinates of $A$: $(3, 4)$
• Coordinates of $B$: $(7, 8)$

From the first condition, we know:

• The $x$-coordinate of $C$ is the same as the $x$-coordinate of $A$, which is $3$. $x_C = 3$

From the second condition, we know:

• The $y$-coordinate of $C$ must be greater than $3$ (the $x$-coordinate of $A$) and less than $8$ (the $y$-coordinate of $B$). $3 < y_C < 8$

From the third condition, we know:

• The coordinates of $C$ must contain one even and one odd value.

Since $x_C = 3$ (an odd number), $y_C$ must be even and must satisfy $3 < y_C < 8$.

Possible Values for $y_C$:

The possible even values for $y_C$ between $3$ and $8$ are $4$ and $6$.

Conclusion:

The coordinates of $C$ that satisfy all conditions are:

• $(3, 4)$
• $(3, 6)$

Since $(3, 4)$ is the location of point $A$, it cannot be $C$. Therefore, the only valid coordinate for $C$ is: $C = (3, 6)$

Would you like further details or have any questions?

Related Questions:

1. What would be the coordinates of point $C$ if the $x$-coordinate had to match point $B$ instead?
2. How many other points can satisfy similar conditions for a different grid setup?
3. If point $C$ had to lie on a line segment between $A$ and $B$, what would be its coordinates?
4. How can you determine a point’s position with constraints on both coordinates?
5. How does the parity (even or odd) of coordinates influence placement on a grid?

Tip:

Always check if each condition in a multi-step problem restricts the possible solutions. This approach narrows down options effectively.