One line passes through the points \( (-2,1) \) and \( (4,9) \). Another line passes through points \( (-3,8) \) and \( (5,2) \). Are the lines parallel, perpendicular, or neither? Choose 1 answer: (A) Parallel (B) Perpendicular (C) Neither

To determine the relationship between the two lines, we first need to find their slopes. The slope (\(m\)) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] For the first line through points \((-2,1)\) and \((4,9)\): \[ m_1 = \frac{9 - 1}{4 - (-2)} = \frac{8}{6} = \frac{4}{3} \] For the second line through points \((-3,8)\) and \((5,2)\): \[ m_2 = \frac{2 - 8}{5 - (-3)} = \frac{-6}{8} = -\frac{3}{4} \] Now, we can check if the lines are parallel, perpendicular, or neither: - Lines are parallel if their slopes are equal. - Lines are perpendicular if the product of their slopes is \(-1\). Calculating the product of the slopes: \[ m_1 \times m_2 = \frac{4}{3} \times -\frac{3}{4} = -1 \] Since the product of the slopes is \(-1\), the two lines are perpendicular. The answer is (B) Perpendicular.