Find the values of m and n, in each case, If:
`(4,-3)` on reflection in x-axis gives `(-m,n)`.

Answer

To find the values of \( m \) and \( n \) when the point \( (4, -3) \) is reflected in the x-axis and gives the point \( (-m, n) \), we can follow these steps:

### Step 1: Understand the reflection in the x-axis
When a point \( (x, y) \) is reflected in the x-axis, the x-coordinate remains the same, while the y-coordinate changes its sign. Thus, the reflection of the point \( (4, -3) \) will be \( (4, 3) \).

### Step 2: Write down the reflected point
From the reflection, we have:
\[ (4, -3) \text{ reflected in the x-axis gives } (4, 3) \]

### Step 3: Set up the equation with the given point
According to the problem, this reflected point \( (4, 3) \) is equal to the point \( (-m, n) \). Therefore, we can write:
\[ (-m, n) = (4, 3) \]

### Step 4: Compare the coordinates
From the equality of the two points, we can compare the x-coordinates and y-coordinates:
1. For the x-coordinates:
\[ -m = 4 \]
2. For the y-coordinates:
\[ n = 3 \]

### Step 5: Solve for \( m \) and \( n \)
1. From \( -m = 4 \):
\[ m = -4 \]
2. From \( n = 3 \):
\[ n = 3 \]

### Final Answer:
Thus, the values are:
\[ m = -4 \quad \text{and} \quad n = 3 \]

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