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. (-4, -2)

Verified step by step guidance

1. Identify the given point as \((-4, -2)\) on the Cartesian coordinate plane.
2. Recall that the point symmetric to a given point with respect to the origin is found by negating both the \(x\) and \(y\) coordinates of the original point.
3. Apply this rule to the point \((-4, -2)\): the symmetric point with respect to the origin will be \((4, 2)\).
4. Plot the original point \((-4, -2)\) on the coordinate plane by moving 4 units left and 2 units down from the origin.
5. Plot the symmetric point \((4, 2)\) by moving 4 units right and 2 units up from the origin.

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 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 is a transformation producing a mirror image of a point or shape across a specific line or point. Reflecting a point about the origin is a specific transformation that changes (x, y) to (-x, -y), helping analyze geometric properties and symmetries.