Which is a listed option for the length of LQ?

• A. 119/11
• B. 77/6
• C. 113/6
• D. 119/6

Answer: (D)

The length of a segment between two points on a plane comes from the distance formula, which is built on the Pythagorean theorem. You take the horizontal difference between L and Q, the vertical difference, square both, add them, and take the square root. When you apply that to the diagram’s coordinates, the result simplifies to 119/6. Since that is exactly the value produced by the distance calculation, it matches the length of LQ and is the correct option. The other fractions don’t arise from the same distance-calculation with the given coordinates, so they don’t represent the true length. If you want to check, plug in the coordinates for L and Q, compute the differences, square and add, then simplify to see the same 119/6 result.