To rotate a shape $90^\circ$ counterclockwise about the origin, you can follow a straightforward process involving the coordinates of each point on the shape. The transformation involves swapping the coordinates and changing the sign of the new x-coordinate.

Specifically, when you rotate a point $(x, y)$ $90^\circ$ counterclockwise about the origin, it is transformed into the new coordinates $(-y, x)$. In this transformation, the original y-coordinate becomes the new x-coordinate (with a negative sign), while the original x-coordinate is now the new y-coordinate.

For instance, consider a point $A$ located at $(3, 4)$. After applying the $90^\circ$ counterclockwise rotation about the origin, the new coordinates of point $A$ will be $(-4, 3)$. This transformation applies to every point of the shape, resulting in a new rotated shape.

To visualize this, imagine the point $(3, 4)$ plotted on a graph. When you rotate it $90^\circ$ counterclockwise, it moves to the left and upward, landing at the new position $(-4, 3)$. This rotation method is consistent and can be applied to all points on the shape, ensuring that the entire shape is rotated accurately.

It is important to note that this rule specifically applies to rotations around the origin. If you need to rotate a shape about a different point, you must first translate the shape so that the point of rotation coincides with the origin. After performing the rotation, you will then need to translate the shape back to its original position.