Which type of joint allows a component to rotate about one axis and translate along a different axis?

The pin-slot joint is the correct answer because it facilitates both rotational and translational motion, which is precisely what the question describes. In a pin-slot joint, one component is allowed to rotate around an axis while being constrained to move along a slot in another component. This combination enables one part to rotate while also translating linearly in a specified direction.

In contrast, a rigid joint does not permit any motion between connected components, as it is designed to maintain a fixed position and orientation. A revolute joint allows for rotation around a single axis but does not permit translation along a different axis. Similarly, a slider joint only allows movement along one axis and lacks the capability for rotational motion.

Thus, the pin-slot joint's unique characteristic of enabling both rotation and translation makes it the appropriate choice for the question presented.