Concept Check Plot each point, and then plot the points that are symmetric to the given point with point with respect to the (a) x-axis (5, -3)

Verified step by step guidance

1. Start by plotting the original point given, which is (5, -3). This means you move 5 units to the right along the x-axis and 3 units down along the y-axis.
2. To find the point symmetric to (5, -3) with respect to the x-axis, recall that reflecting a point over the x-axis changes the sign of the y-coordinate but keeps the x-coordinate the same.
3. Apply this reflection rule: the x-coordinate remains 5, and the y-coordinate changes from -3 to 3, giving the symmetric point (5, 3).
4. Plot the symmetric point (5, 3) on the coordinate plane by moving 5 units to the right and 3 units up from the origin.
5. Verify that the original point and its symmetric point are equidistant from the x-axis but on opposite sides, confirming the reflection is correct.

Key Concepts

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 x-axis

Symmetry about the x-axis means reflecting a point across the x-axis. For a point (x, y), its symmetric point with respect to the x-axis is (x, -y). This flips the point vertically while keeping the horizontal position unchanged.

Reflection of Points

Reflection involves creating a mirror image of a point across a specific axis. In this case, reflecting across the x-axis changes the sign of the y-coordinate but leaves the x-coordinate the same. Understanding reflection helps in visualizing geometric transformations.