Final answer:
The line through points P(7,5) and Q(1,-3) is perpendicular to the line through points R(-10,7) and S(-18,13).
Step-by-step explanation:
To determine if the line through points P(7,5) and Q(1,-3) is perpendicular, parallel, or neither to the line through points R(-10,7) and S(-18,13), we need to find the slopes of both lines. The slope of a line passing through two points (x1,y1) and (x2,y2) is given by the formula m = (y2 - y1)/(x2 - x1).
For the line through P(7,5) and Q(1,-3), the slope is m = (-3 - 5)/(1 - 7) = (-8)/(-6) = 4/3.
For the line through R(-10,7) and S(-18,13), the slope is m = (13 - 7)/(-18 - (-10)) = 6/(-8) = -3/4.
Since the slopes of the two lines are negative reciprocals of each other (4/3 and -3/4), the lines are perpendicular to each other.