Final answer:
The shortest line segment that passes through point (a, b) in the first quadrant is the hypotenuse of a right triangle with legs a and b, calculated using the Pythagorean theorem as c = √(a² + b²).
Step-by-step explanation:
The question involves finding the length of the shortest line segment in the first quadrant that passes through a given point (a, b). By interpreting the given point as forming a right triangle where (a, b) are the legs of the triangle, we can apply the Pythagorean theorem to find the length of the hypotenuse, which is the shortest line segment from the origin to the point.
The Pythagorean theorem states that a² + b² = c², where a and b are the legs of the triangle and c is the hypotenuse. To solve for the hypotenuse, we take the square root of the sum of the squares of a and b. Therefore, the length of the shortest line segment is c = √(a² + b²).