Question

Is the line through P(7,5) and Q(1, -3) perpendicular, parallel, or neither to the line through points R(-10, 7) and S(-18, 13)? Explain.

Answer 1

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.