Final answer:
To calculate the length of a line segment using the Pythagorean theorem, we need the coordinates of the endpoint. Without this information, it's impossible to provide the length in radical form.
Step-by-step explanation:
To find the length of a line segment whose endpoints are the origin and another point, we use the Pythagorean theorem, as the line segment represents the hypotenuse of a right triangle formed by the x and y coordinates of the endpoint as the legs. The theorem is expressed as:
c = √(a² + b²)
However, the problem does not specify the coordinates. With the information given, we cannot determine the length in simplest radical form without additional data about the endpoints. To provide an answer, we would need the exact coordinates of the endpoint in question.
If we take an example with hypothetical coordinates, such as (3, 4) where 3 and 4 are the lengths of the legs, we'd use the equation:
c = √(3² + 4²) = √(9 + 16) = √25 = 5
But this is just an example, and we need the actual coordinates to solve the problem correctly.