For two perpendicular lines, which statement is correct about their slopes?

For two perpendicular lines, which statement is correct about their slopes?

• A. Slopes are equal
• B. Slopes are opposite reciprocals
• C. Slopes are both zero
• D. Slopes are both undefined

Answer: (B)

When two lines are perpendicular, the way their steepness relates to each other is that their slopes multiply to -1. If one line has slope m, the slope of a line perpendicular to it is -1/m (as long as neither line is vertical or horizontal). This comes from how angles work with slopes: the angle a line makes with the x-axis has tangent equal to the slope, and perpendicular angles add to 90°, so tan(θ2) = tan(θ1 + 90°) = -cot(θ1) = -1/tan(θ1). So the two slopes are opposite reciprocals. If one line is horizontal (slope 0) and the other is vertical (undefined), they’re still perpendicular, but you can’t multiply 0 by undefined; the main idea is the negative reciprocal relationship generally.

When two lines are perpendicular, the way their steepness relates to each other is that their slopes multiply to -1. If one line has slope m, the slope of a line perpendicular to it is -1/m (as long as neither line is vertical or horizontal). This comes from how angles work with slopes: the angle a line makes with the x-axis has tangent equal to the slope, and perpendicular angles add to 90°, so tan(θ2) = tan(θ1 + 90°) = -cot(θ1) = -1/tan(θ1). So the two slopes are opposite reciprocals. If one line is horizontal (slope 0) and the other is vertical (undefined), they’re still perpendicular, but you can’t multiply 0 by undefined; the main idea is the negative reciprocal relationship generally.