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A point P is reflected in the origin. Co...

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

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To find the coordinates of point P given that its image after reflection in the origin is (-2, 7), we can follow these steps: 1. **Understand the reflection in the origin**: When a point (x, y) is reflected in the origin, its coordinates change to (-x, -y). This means that if we know the coordinates of the reflected point, we can find the original point by reversing the signs of the coordinates. 2. **Set up the equations**: Let the coordinates of point P be (x, y). After reflection, the coordinates become (-x, -y). We know the coordinates of the image (reflected point) are (-2, 7). Therefore, we can set up the following equations: - -x = -2 - -y = 7 3. **Solve for x**: From the first equation, we can solve for x: - -x = -2 - Multiply both sides by -1: - x = 2 4. **Solve for y**: From the second equation, we can solve for y: - -y = 7 - Multiply both sides by -1: - y = -7 5. **Combine the results**: Now that we have both x and y, we can write the coordinates of point P: - P = (x, y) = (2, -7) Thus, the coordinates of point P are (2, -7).
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