Here are the essential concepts you must grasp in order to answer the question correctly.
Symmetry with respect to the x-axis
A point (x, y) is symmetric to the x-axis if its reflection across the x-axis is (x, -y). This means that the x-coordinate remains the same while the y-coordinate changes sign. For example, the point (-4, -2) would reflect to (-4, 2) when considering symmetry about the x-axis.
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Symmetry with respect to the y-axis
A point (x, y) is symmetric to the y-axis if its reflection across the y-axis is (-x, y). In this case, the y-coordinate remains unchanged while the x-coordinate changes sign. For the point (-4, -2), the symmetric point with respect to the y-axis would be (4, -2).
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Symmetry with respect to the origin
A point (x, y) is symmetric to the origin if its reflection through the origin is (-x, -y). This transformation involves changing the signs of both coordinates. For the point (-4, -2), the symmetric point with respect to the origin would be (4, 2).
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Graph Hyperbolas NOT at the Origin