A point P is reflected in the origin. Co-ordinates of its image are (-2, 7).
Find the co-ordinates of the image of P under reflection in the x-axis.

Answer

To find the coordinates of the image of point P under reflection in the x-axis, we will follow these steps:

### Step 1: Identify the coordinates of point P
We know that the image of point P after reflection in the origin is given as (-2, 7). We need to find the original coordinates of point P.

### Step 2: Use the reflection formula for the origin
When a point (x, y) is reflected in the origin, the new coordinates become (-x, -y). Given that the image after reflection in the origin is (-2, 7), we can set up the following equations:
- -x = -2
- -y = 7

### Step 3: Solve for x and y
From the equations:
1. -x = -2 implies x = 2
2. -y = 7 implies y = -7

Thus, the coordinates of point P are (2, -7).

### Step 4: Reflect point P in the x-axis
When a point (x, y) is reflected in the x-axis, the x-coordinate remains the same, and the y-coordinate changes sign. Therefore, the reflection of point P (2, -7) in the x-axis will be:
- x-coordinate: 2 (remains the same)
- y-coordinate: -(-7) = 7 (changes sign)

### Step 5: Write the coordinates of the image
The coordinates of the image of point P under reflection in the x-axis are (2, 7).

### Final Answer:
The coordinates of the image of P under reflection in the x-axis are (2, 7).

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