Question

Decide whether Line 1 and Line 2 are parallel, perpendicular, or neither. Line 1 passes through (5, -9) and (0, -5) Line 2 passes through (-3, 8) and (1, 3)

Answer 1

Line 1 and Line 2 are perpendicular to each other because the slope of Line 1 is -4/5 and the slope of Line 2 is -5/4, which are negative reciprocals.

Step-by-step explanation:

To decide whether Line 1 and Line 2 are parallel, perpendicular, or neither, we need to determine the slopes of both lines. The slope of a line is calculated by the change in the y-coordinate divided by the change in the x-coordinate between two points on the line (rise/run).

For Line 1, which passes through the points (5, -9) and (0, -5), the slope can be calculated as follows:

• Slope of Line 1 = (y2 - y1) / (x2 - x1)
• Slope of Line 1 = (-5 + 9) / (0 - 5)
• Slope of Line 1 = 4 / -5
• Slope of Line 1 = -4/5

For Line 2, which passes through the points (-3, 8) and (1, 3), the slope is calculated similarly:

• Slope of Line 2 = (y2 - y1) / (x2 - x1)
• Slope of Line 2 = (3 - 8) / (1 + 3)
• Slope of Line 2 = -5 / 4
• Slope of Line 2 = -5/4

Since the slopes of Line 1 and Line 2 are negative reciprocals of each other (i.e., -4/5 and -5/4), this means that the lines are perpendicular to each other.