Two points for each of two lines are given. Determine if the lines are parallel, perpendicular, or neither.
L1: (4, -6) and (3, -2)
L2: (3, -1) and (7, 0)
To determine if two lines are parallel, perpendicular, or neither, we can use the slopes of the lines. The formula for the slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slopes of the two lines:
L1: (4, -6) and (3, -2)
slope_L1 = (-2 - (-6)) / (3 - 4)
= (-2 + 6) / (-1)
= 4 / (-1)
= -4
L2: (3, -1) and (7, 0)
slope_L2 = (0 - (-1)) / (7 - 3)
= (0 + 1) / 4
= 1 / 4
Now we compare the slopes:
- If the slopes are equal, the lines are parallel.
- If the slopes are negative reciprocals of each other, the lines are perpendicular.
- If the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
In this case, the slope of L1 is -4 and the slope of L2 is 1/4. Since the slopes are neither equal nor negative reciprocals, we can conclude that the lines L1 and L2 are neither parallel nor perpendicular to each other.