Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis, (b) y-axis, and (c) origin. (5, -3)

Verified step by step guidance

1. Step 1: Start by plotting the given point (5, -3) on the Cartesian plane. This point is located 5 units to the right of the origin along the x-axis and 3 units below the origin along the y-axis.
2. Step 2: To find the point that is symmetric to (5, -3) with respect to the x-axis, you need to change the sign of the y-coordinate while keeping the x-coordinate the same. This gives you the point (5, 3). Plot this point on the same Cartesian plane.
3. Step 3: To find the point that is symmetric to (5, -3) with respect to the y-axis, you need to change the sign of the x-coordinate while keeping the y-coordinate the same. This gives you the point (-5, -3). Plot this point on the same Cartesian plane.
4. Step 4: To find the point that is symmetric to (5, -3) with respect to the origin, you need to change the signs of both the x-coordinate and the y-coordinate. This gives you the point (-5, 3). Plot this point on the same Cartesian plane.
5. Step 5: Now you have plotted the original point and its three symmetric points with respect to the x-axis, y-axis, and the origin. This will give you a visual representation of how these symmetries work in the Cartesian plane.

Key Concepts

Symmetry with respect to the x-axis

A point (x, y) is symmetric to the x-axis if its reflection across the x-axis is (x, -y). This means that the x-coordinate remains the same while the y-coordinate changes sign. For example, the point (5, -3) would have its symmetric point with respect to the x-axis at (5, 3).

Symmetry with respect to the y-axis

A point (x, y) is symmetric to the y-axis if its reflection across the y-axis is (-x, y). In this case, the y-coordinate remains unchanged while the x-coordinate changes sign. For the point (5, -3), the symmetric point with respect to the y-axis would be (-5, -3).

Symmetry with respect to the origin

A point (x, y) is symmetric to the origin if its reflection across the origin is (-x, -y). This transformation involves changing the signs of both coordinates. For the point (5, -3), the symmetric point with respect to the origin would be (-5, 3).