Final answer:
To determine if two lines are perpendicular, we can calculate their slopes. The line through P(1,9) and Q(9,6) has a slope of -3/8, and the line through R(-6,0) and S(-9,8) has a slope of -8/3. The product of these slopes is -1, indicating that the lines are perpendicular.
Step-by-step explanation:
To determine whether the line through points P(1,9) and Q(9,6) is perpendicular to the line through points R(-6,0) and S(-9,8), we can calculate the slope of each line. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: slope = (y2 - y1) / (x2 - x1).
For the line through P(1,9) and Q(9,6), the slope is (6 - 9) / (9 - 1) = -3/8.
For the line through R(-6,0) and S(-9,8), the slope is (8 - 0) / (-9 - (-6)) = 8/-3 = -8/3.
If the two lines are perpendicular, the product of their slopes should be -1. Let's check: (-3/8) * (-8/3) = 1. Therefore, the line through points P(1,9) and Q(9,6) is perpendicular to the line through points R(-6,0) and S(-9,8).