Question

Line 1: (0, 1), (1,4)

Line 2: (3, 2), (6,3)
Are the given lines parallel, perpendicular, or neither?

a) Parallel
b) Perpendicular
c) Neither
d) None of the above

Answer 1

The given lines are neither parallel nor perpendicular.

Step-by-step explanation:

The given lines are not parallel or perpendicular to each other. To determine if two lines are parallel, we compare their slopes. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals of each other, the lines are perpendicular. First, we find the slope of the first line using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the given coordinates, we get:

m1 = (4 - 1) / (1 - 0) = 3

Similarly, we find the slope of the second line:

m2 = (3 - 2) / (6 - 3) = 1/3

Since the slopes of the lines are not equal and not negative reciprocals, the lines are neither parallel nor perpendicular.