Concept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (c) origin. (5, -3)

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Understand that symmetry with respect to the origin means reflecting the point through the origin, which changes both the x-coordinate and y-coordinate to their opposites.

Start by plotting the original point (5, -3) on the coordinate plane: move 5 units to the right on the x-axis and 3 units down on the y-axis.

To find the point symmetric to (5, -3) with respect to the origin, apply the transformation: \((x, y) \rightarrow (-x, -y)\).

Calculate the symmetric point by changing the signs of both coordinates: \((-5, 3)\).

Plot the symmetric point (-5, 3) on the coordinate plane: move 5 units to the left on the x-axis and 3 units up on the y-axis.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Coordinate Plane and Plotting Points

The coordinate plane is a two-dimensional surface defined by the x-axis (horizontal) and y-axis (vertical). Each point is represented by an ordered pair (x, y), where x indicates the horizontal position and y the vertical position. Plotting a point involves locating its position based on these coordinates.

Symmetry with Respect to the Origin

Symmetry about the origin means that for any point (x, y), its symmetric point is (-x, -y). This reflects the point through the origin, effectively rotating it 180 degrees around (0,0). It is a key concept in understanding transformations in the coordinate plane.

Reflection and Transformation in the Coordinate Plane

Reflection involves flipping a point across a line or point, creating a mirror image. In this case, reflecting a point about the origin is a specific transformation that changes the sign of both coordinates. Understanding these transformations helps in visualizing geometric relationships and solving related problems.

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