P and Q have co-ordinates (0, 5) and (-2, 4).
Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x-axis.

Answer

To solve the problem of finding the coordinates of the image of point Q after reflecting it in the origin and then in the x-axis, we can follow these steps:

### Step 1: Identify the coordinates of point Q
Point Q has coordinates (-2, 4).

### Step 2: Reflect point Q in the origin
To reflect a point (x, y) in the origin, we change the signs of both coordinates. Therefore, the reflection of Q (-2, 4) in the origin will be:
- New x-coordinate: -(-2) = 2
- New y-coordinate: -(4) = -4

So, the coordinates of the image of Q after reflection in the origin (let's call it Q') are (2, -4).

### Step 3: Reflect point Q' in the x-axis
To reflect a point (x, y) in the x-axis, we keep the x-coordinate the same and change the sign of the y-coordinate. Therefore, the reflection of Q' (2, -4) in the x-axis will be:
- New x-coordinate: 2 (remains the same)
- New y-coordinate: -(-4) = 4

So, the coordinates of the image of Q after reflecting in the x-axis (let's call it Q'') are (2, 4).

### Final Answer:
The coordinates of the image of Q obtained by reflecting it in the origin followed by reflection in the x-axis are (2, 4).

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