Question

The slope of line bis 3

Which lines are perpendicular to line b?
Select each correct answer.
line d, which contains the points (1, -2) and (10, -14)
line c, which contains the points (6, 5) and (10, 2)
line e, which contains the points (-2, 3) and (-10, 9)
line a, which contains the points (4, 1) and (7,5)

Answer 1

To determine which lines are perpendicular to line b, we need to find lines that have a slope that is the negative reciprocal of the slope of line b.

Given that the slope of line b is 3, the negative reciprocal of 3 is -1/3.

Now let's analyze each line:

line d: slope = (-14 - (-2)) / (10 - 1) = -12 / 9 = -4/3
Since the slope of line d (-4/3) is not the negative reciprocal of the slope of line b (-1/3), line d is not perpendicular to line b.

line c: slope = (2 - 5) / (10 - 6) = -3 / 4
Since the slope of line c (-3/4) is not the negative reciprocal of the slope of line b (-1/3), line c is not perpendicular to line b.

line e: slope = (9 - 3) / (-10 - (-2)) = 6 / -8 = -3/4
Since the slope of line e (-3/4) is the negative reciprocal of the slope of line b (-1/3), line e is perpendicular to line b.

line a: slope = (5 - 1) / (7 - 4) = 4 / 3
Since the slope of line a (4/3) is not the negative reciprocal of the slope of line b (-1/3), line a is not perpendicular to line b.

Based on the analysis, the correct answer is:

- line e, which contains the points (-2, 3) and (-10, 9)