One line passes through the points \( (-7,-4) \) and \( (5,4) \). Another line passes through points \( (-4,6) \) and \( (6,-9) \). 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. For the line through points \( (-7,-4) \) and \( (5,4) \): \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - (-4)}{5 - (-7)} = \frac{4 + 4}{5 + 7} = \frac{8}{12} = \frac{2}{3} \] For the line through points \( (-4,6) \) and \( (6,-9) \): \[ \text{slope} = \frac{-9 - 6}{6 - (-4)} = \frac{-15}{10} = -\frac{3}{2} \] Now, we compare the slopes: The product of the two slopes is: \[ \left(\frac{2}{3}\right) \times \left(-\frac{3}{2}\right) = -1 \] Since the product of the slopes is -1, the two lines are perpendicular. Thus, the answer is (B) Perpendicular.