Which statement describes the slopes of perpendicular lines?

Which statement describes the slopes of perpendicular lines?

• A. have slopes that are equal.
• B. have slopes that are negative reciprocals of each other.
• C. intersect at right angles only if they are also parallel.
• D. have slopes that are reciprocals of each other.

Answer: (B)

Perpendicular lines have slopes that are negative reciprocals of each other. If one line has slope m, the other must have slope -1/m (as long as neither line is vertical). This relationship makes their product equal to -1, which guarantees the lines cross at a right angle. For example, slopes 3 and -1/3 form a right angle. The idea also fits the horizontal-vertical case: a horizontal line (slope 0) and a vertical line (undefined slope) are perpendicular, even though you can’t express that pair with a numeric reciprocal. The other statements don’t describe this right-angle relationship: equal slopes imply parallel lines, not perpendicular; perpendicular lines intersect (not merely if they’re parallel); and just reciprocals without the negative sign don’t generally produce a right angle.

Perpendicular lines have slopes that are negative reciprocals of each other. If one line has slope m, the other must have slope -1/m (as long as neither line is vertical). This relationship makes their product equal to -1, which guarantees the lines cross at a right angle. For example, slopes 3 and -1/3 form a right angle. The idea also fits the horizontal-vertical case: a horizontal line (slope 0) and a vertical line (undefined slope) are perpendicular, even though you can’t express that pair with a numeric reciprocal. The other statements don’t describe this right-angle relationship: equal slopes imply parallel lines, not perpendicular; perpendicular lines intersect (not merely if they’re parallel); and just reciprocals without the negative sign don’t generally produce a right angle.