Sure! To solve this problem, let's first understand what happens when we rotate a point around the origin by 180 degrees.
When you rotate a point by 180 degrees, it changes its quadrant in the Cartesian Plane. If the point starts in Quadrant I (both coordinates being positive), after the rotation, it will end up in Quadrant III (both coordinates negative). Similarly, a point in Quadrant II (x negative, y positive), such as our point A(-2,3), will end up in Quadrant IV (x positive, y negative) after the rotation.
The mathematical relationship between the original and rotated coordinates is given by multiplying all of them by -1.
Let's apply these transformations to our point A(-2,3):
Multiply the x-coordinate of point A(-2,3) by -1. This will give us a new x-coordinate of 2.
Multiply the y-coordinate of point A(-2,3) by -1. This will give us a new y-coordinate of -3.
So, after a 180-degree rotation about the origin, the given point A(-2,3) becomes the point (2,-3).