Final answer:
In Euclidean geometry, exactly one straight line can be drawn through any two distinct points, hence the answer to the quiz question is one line through points J and K.
Step-by-step explanation:
Based on the principles of Euclidean geometry, through any two points, there can be exactly one straight line. When we consider points J and K lying in plane H, regardless of where they are placed in that plane, only one line can pass through both of them. Therefore, the correct answer to the question is that there can be only one line drawn through points J and K. This is a fundamental concept in geometry, often used in conjunction with other geometric principles such as the Pythagorean theorem where the shortest distance between two points is a straight line.