Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis, (b) y-axis, and (c) origin. (5, -3)

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Identify the given point as \( (5, -3) \). This means the point is located 5 units to the right of the origin along the x-axis and 3 units down along the y-axis.

To find the point symmetric with respect to the x-axis, keep the x-coordinate the same and change the sign of the y-coordinate. The symmetric point will be \( (5, 3) \).

To find the point symmetric with respect to the y-axis, keep the y-coordinate the same and change the sign of the x-coordinate. The symmetric point will be \( (-5, -3) \).

To find the point symmetric with respect to the origin, change the signs of both the x- and y-coordinates. The symmetric point will be \( (-5, 3) \).

Plot all points on the coordinate plane: the original point \( (5, -3) \), the x-axis symmetric point \( (5, 3) \), the y-axis symmetric point \( (-5, -3) \), and the origin symmetric point \( (-5, 3) \).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Coordinate Plane and Plotting Points

The coordinate plane consists of two perpendicular number lines called the x-axis and y-axis. Points are plotted using ordered pairs (x, y), where x indicates horizontal position and y indicates vertical position. Understanding how to locate and plot points is fundamental for visualizing symmetry.

Symmetry with Respect to the Axes

Symmetry about the x-axis means reflecting a point across the x-axis, changing the sign of the y-coordinate while keeping x the same. Symmetry about the y-axis involves changing the sign of the x-coordinate while keeping y the same. These reflections produce mirror images of the original point.

Symmetry with Respect to the Origin

Symmetry about the origin reflects a point through the origin, changing the signs of both coordinates. For a point (x, y), its symmetric point with respect to the origin is (-x, -y). This transformation is equivalent to a 180-degree rotation around the origin.