Graphs 5
2 marks · NormalExplain why the product of the gradients of two perpendicular lines (neither vertical nor horizontal) is always -1.
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Because if two lines are perpendicular, their gradients m1 and m2 satisfy m1 × m2 = –1
Also accept: The gradients multiply to –1 for perpendicular lines
Common mistakes: Confusing with parallel lines
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Marking points
B1 · 2 marks · Explains the negative reciprocal property and/or states m1 × m2 = -1 for perpendicular lines
Worked solution
For two lines to be perpendicular, one must have the negative reciprocal gradient of the other (m2 = –1/m1). Multiplying the gradients gives m1 × m2 = m1 × (–1/m1) = –1.