The point (a,-a) does not lie on the graph of

Options

A. x=a
B. y=-a
C. y=x
D. x+y=0

Answer

To determine whether the point (a, -a) lies on the graph of the given equations, we will substitute the coordinates of the point into each equation and check if the left-hand side (LHS) equals the right-hand side (RHS). If they do not equal, it means the point does not lie on that graph.

### Step-by-Step Solution:

1. **Identify the point and equations**:
We have the point (a, -a) and we need to check it against the equations provided.

2. **First equation**: \( x = a \)
- Substitute \( x = a \) into the equation.
- LHS = a (from the point) and RHS = a (from the equation).
- Since LHS = RHS, the point (a, -a) lies on this graph.

3. **Second equation**: \( y = -a \)
- Substitute \( y = -a \) into the equation.
- LHS = -a (from the point) and RHS = -a (from the equation).
- Since LHS = RHS, the point (a, -a) lies on this graph.

4. **Third equation**: \( y = x \)
- Substitute \( y = -a \) and \( x = a \) into the equation.
- LHS = -a (from the point) and RHS = a (from the equation).
- Since LHS ≠ RHS, the point (a, -a) does not lie on this graph.

5. **Conclusion**:
The point (a, -a) does not lie on the graph of the equation \( y = x \).

### Final Answer:
The point (a, -a) does not lie on the graph of the equation \( y = x \).