Concept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (b) y-axis. (-4, -2)

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Identify the given point as \((-4, -2)\), where \(-4\) is the x-coordinate and \(-2\) is the y-coordinate.

Recall that reflecting a point across the y-axis changes the sign of the x-coordinate but keeps the y-coordinate the same.

Apply this rule to the point \((-4, -2)\): the x-coordinate becomes \(4\) (the opposite sign), and the y-coordinate remains \(-2\).

Write the coordinates of the symmetric point with respect to the y-axis as \((4, -2)\).

Plot both points on the coordinate plane: the original point \((-4, -2)\) and its reflection \((4, -2)\), ensuring they are equidistant from the y-axis but on opposite sides.

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Concetti chiave

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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 horizontal position and y indicates vertical position. Plotting a point involves locating its position based on these coordinates.

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Convert Points from Polar to Rectangular

Symmetry with Respect to the y-axis

Symmetry about the y-axis means that for any point (x, y), its symmetric point has coordinates (-x, y). This reflects the point across the vertical y-axis, changing the sign of the x-coordinate while keeping the y-coordinate the same.

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Even and Odd Identities

Reflection of Points

Reflection is a transformation producing a mirror image of a point or shape across a specific line, such as the y-axis. Understanding reflection helps in visualizing how points move and change coordinates when mirrored, which is essential for plotting symmetric points.

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