One line passes through the points \( (2,1) \) and \( (5,7) \). Another line passes through points \( (-3,8) \) and \( (8,3) \). Are the lines parallel, perpendicular, or neither? Choose 1 answer: (A) Parallel (B) Perpendicular (C) Neither

- Calculate the slope of the line passing through \((2,1)\) and \((5,7)\): \[ m_1 = \frac{7 - 1}{5 - 2} = \frac{6}{3} = 2. \] - Calculate the slope of the line passing through \((-3,8)\) and \((8,3)\): \[ m_2 = \frac{3 - 8}{8 - (-3)} = \frac{-5}{11}. \] - Check if the lines are parallel. Lines are parallel if their slopes are equal: \[ 2 \neq \frac{-5}{11}. \] - Check if the lines are perpendicular. Lines are perpendicular if the product of their slopes is \(-1\): \[ 2 \cdot \frac{-5}{11} = \frac{-10}{11} \neq -1. \] - Since the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular. Answer: (C) Neither.