Final answer:
Line segment AB can be transformed by a reflection over the x-axis, a rotation of 90 degrees counterclockwise about the origin, a translation 3 units to the right and 2 units up, and an enlargement by a scale factor of 2 centered at the origin.
Step-by-step explanation:
a. Reflection over the x-axis: In a reflection over the x-axis, each y-coordinate of the points on the line segment AB will change signs. The x-coordinate of each point will stay the same. For example, if AB passes through point (2, 3), in a reflection over the x-axis, it will pass through point (2, -3).
b. Rotation of 90 degrees counterclockwise about the origin: In a rotation of 90 degrees counterclockwise about the origin, the x-coordinate of each point on the line segment AB becomes the negative of its y-coordinate, and the y-coordinate becomes the positive of its x-coordinate. For example, if AB passes through point (2, 3), after the rotation it will pass through point (-3, 2).
c. Translation 3 units to the right and 2 units up: In a translation 3 units to the right and 2 units up, each point on the line segment AB will move 3 units to the right and 2 units up, maintaining the same direction and length. For example, if AB passes through point (2, 3), after the translation it will pass through point (5, 5).
d. Enlargement by a scale factor of 2 centered at the origin: In an enlargement by a scale factor of 2 centered at the origin, each point on the line segment AB will move away from the origin, while maintaining the same direction and doubling its distance from the origin. For example, if AB passes through point (2, 3), after the enlargement it will pass through point (4, 6).