The point symmetric to (00,99) with respect to the origin is
The correct answer and explanation is:
The symmetric point to (0, 99) with respect to the origin is (0, -99).
Explanation:
To find the symmetric point of a given point with respect to the origin, we perform the following transformation:
- Reflection Across the Origin: The origin (0, 0) acts as the center of reflection. For any point (x, y), the point symmetric to it with respect to the origin will have the coordinates (-x, -y). This is because when a point is reflected across the origin, its x and y coordinates change signs.
- Application to the Given Point: In this case, the point given is (0, 99). Using the formula for symmetry across the origin, we change the sign of both coordinates:
- The x-coordinate of the point is 0, and since the negative of 0 is still 0, the x-coordinate of the symmetric point remains 0.
- The y-coordinate of the point is 99, and the negative of 99 is -99. Therefore, the y-coordinate of the symmetric point becomes -99.
- Conclusion: The symmetric point to (0, 99) with respect to the origin is (0, -99).
This concept is essential in geometry and is used in various applications such as reflection symmetry, transformations, and understanding coordinate geometry. The operation of reflecting a point across the origin can be applied to any point in two-dimensional space to find its symmetric counterpart.