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A point P is reflected in the x-axis. Co...

A point P is reflected in the x-axis. Co-ordinates of its image are (-4, 5).
Find the co-ordinates of P.

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To find the coordinates of point P given that its image after reflection in the x-axis is (-4, 5), we can follow these steps: 1. **Understand the reflection in the x-axis**: When a point P with coordinates (x, y) is reflected in the x-axis, the coordinates of its image become (x, -y). This means that only the y-coordinate changes sign. 2. **Identify the coordinates of the image**: According to the problem, the coordinates of the image after reflection are given as (-4, 5). 3. **Set up the equations**: From the reflection property, we know: - The x-coordinate remains the same: \( x = -4 \) - The y-coordinate changes sign: \( -y = 5 \) 4. **Solve for y**: From the equation \( -y = 5 \), we can solve for y: \[ y = -5 \] 5. **Combine the results**: Now that we have both coordinates, we can write the coordinates of point P: \[ P = (x, y) = (-4, -5) \] Therefore, the coordinates of point P are **(-4, -5)**.
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