If a line has slope m and another line is perpendicular to it (neither line is vertical), what is the slope of the other line?

If a line has slope m and another line is perpendicular to it (neither line is vertical), what is the slope of the other line?

• A. m
• B. -1/m
• C. 0
• D. 1/m

Answer: (B)

A line perpendicular to a given non-vertical line has slope equal to the negative reciprocal of the given slope. If the first line has slope m, the second line’s slope is -1/m. This comes from thinking in terms of angles: the slope is tan of the angle with the x-axis, and a perpendicular line has that angle plus 90 degrees, whose tangent is -cotangent, i.e., -1/m. This only makes sense when m is finite (not vertical) and not zero (since a horizontal line would make the perpendicular vertical). So the slope of the other line is the negative reciprocal of m, namely -1/m. For example, if m = 2, the perpendicular slope is -1/2; if m = -3, it’s 1/3.

A line perpendicular to a given non-vertical line has slope equal to the negative reciprocal of the given slope. If the first line has slope m, the second line’s slope is -1/m. This comes from thinking in terms of angles: the slope is tan of the angle with the x-axis, and a perpendicular line has that angle plus 90 degrees, whose tangent is -cotangent, i.e., -1/m. This only makes sense when m is finite (not vertical) and not zero (since a horizontal line would make the perpendicular vertical). So the slope of the other line is the negative reciprocal of m, namely -1/m. For example, if m = 2, the perpendicular slope is -1/2; if m = -3, it’s 1/3.