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 (5, -3)

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Identify the given point as \((5, -3)\), where \(5\) is the \(x\)-coordinate and \(-3\) is the \(y\)-coordinate.

Recall that symmetry with respect to the \(y\)-axis means reflecting the point across the \(y\)-axis. This changes the sign of the \(x\)-coordinate but keeps the \(y\)-coordinate the same.

Apply the reflection rule: For a point \((x, y)\), its symmetric point with respect to the \(y\)-axis is \((-x, y)\).

Using this rule, find the symmetric point of \((5, -3)\) by changing the \(x\)-coordinate from \(5\) to \(-5\), while keeping the \(y\)-coordinate \(-3\) unchanged. So, the symmetric point is \((-5, -3)\).

Plot both points on the coordinate plane: the original point \((5, -3)\) on the right side of the \(y\)-axis, and the symmetric point \((-5, -3)\) on the left side, at the same vertical level.

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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 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.

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.

Reflection of Points in the Coordinate Plane

Reflection involves creating a mirror image of a point across a specific axis. For the y-axis, reflection changes the x-coordinate's sign but leaves the y-coordinate unchanged. Understanding reflections helps in visualizing geometric transformations and solving related problems.