Question

M1 represents the slope of line 1, and m2 represents the slope of the distinct line, line 2. Indicate whether line 1 and line 2 are parallel, perpendicular, or neither. M1 = 5/2, M2 = -2/5?

1) Parallel
2) Perpendicular
3) Neither

Answer 1

Line 1 with slope M1 = 5/2 and line 2 with slope M2 = -2/5 are perpendicular because the slopes are negative reciprocals of each other.

Step-by-step explanation:

The student's question is about determining whether two lines are parallel, perpendicular, or neither based on their slopes. With M1 representing the slope of line 1, and M2 representing the slope of line 2, the values given are M1 = 5/2, and M2 = -2/5. In geometry, two non-vertical lines are perpendicular if the product of their slopes is -1. This occurs when one slope is the negative reciprocal of the other. Since 5/2 is the negative reciprocal of -2/5, line 1 with slope M1 = 5/2 and line 2 with slope M2 = -2/5 are perpendicular. Therefore, the correct answer to whether lines 1 and 2 are parallel, perpendicular, or neither is option 2) Perpendicular.