Question

P(-4, 17), Q(1, -3), R(-9, 3), S(-5, 4)

Use slope to determine if lines PQ and RS are parallel, perpendicular, or neither. Slope of line
Slope of line RS is ________

Answer 1

Lines PQ and RS are neither parallel nor perpendicular because their slopes, -4 and 0.25 respectively, are neither equal nor negative reciprocals of each other.

Step-by-step explanation:

To determine if lines PQ and RS are parallel, perpendicular, or neither, we must calculate the slope of each line. The slope is calculated as the ratio of the change in the y-coordinates to the change in the x-coordinates between two points on a line. For line PQ, we use the points P(-4, 17) and Q(1, -3). For line RS, we use points R(-9, 3) and S(-5, 4).

The slope of line PQ is calculated as follows:

Slope of PQ = (y2 - y1) / (x2 - x1)

= (-3 - 17) / (1 - (-4))

= (-20) / (5)

= -4

The slope of line RS is calculated as follows:

Slope of RS = (y2 - y1) / (x2 - x1)

= (4 - 3) / (-5 - (-9))

= (1) / (4)

= 0.25

Since the slopes of PQ and RS are not equal, lines PQ and RS are not parallel. The slopes are not negative reciprocals of each other (since -4 is not equal to -1/0.25), so the lines are neither perpendicular. Therefore, lines PQ and RS are neither parallel nor perpendicular.