If a line is perpendicular to a line with slope -2, what is the slope of the perpendicular line?

If a line is perpendicular to a line with slope -2, what is the slope of the perpendicular line?

• A. 2
• B. -2
• C. -1/2
• D. 1/2

Answer: (D)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if one line has slope m, the slope of a line perpendicular to it is -1/m. Here, the given slope is -2, so the perpendicular slope is -1/(-2) = 1/2. You can check by multiplying: (-2) × (1/2) = -1, which confirms perpendicularity. A slope of 2 would give a product of -4 with -2, not -1, so it isn’t perpendicular. A slope of -2 would make the lines parallel, not perpendicular. A slope of -1/2 would yield a product of 1 with -2, also not perpendicular.

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if one line has slope m, the slope of a line perpendicular to it is -1/m.

Here, the given slope is -2, so the perpendicular slope is -1/(-2) = 1/2. You can check by multiplying: (-2) × (1/2) = -1, which confirms perpendicularity.

A slope of 2 would give a product of -4 with -2, not -1, so it isn’t perpendicular. A slope of -2 would make the lines parallel, not perpendicular. A slope of -1/2 would yield a product of 1 with -2, also not perpendicular.