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Summary

DescriptionSlopes and orthogonality.svg
English: The two triangles are similar (but not congruent) because the angles are the same. For line 1, the "run" Δ x 1 {\displaystyle \Delta x_{1}} {\displaystyle \Delta x_{1}} is negative, as shown. Setting the ratios equal yields − m 1 = Δ y 1 / Δ x 1 = Δ x 2 / Δ y 2 = 1 / m 2 . {\displaystyle -m_{1}=\Delta y_{1}/\Delta x_{1}=\Delta x_{2}/\Delta y_{2}=1/m_{2}.} {\displaystyle -m_{1}=\Delta y_{1}/\Delta x_{1}=\Delta x_{2}/\Delta y_{2}=1/m_{2}.} Therefore m 1 m 2 = − 1 {\displaystyle m_{1}m_{2}=-1} {\displaystyle m_{1}m_{2}=-1}
Date
Source Own work
Author Guy vandegrift

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Captions

Proof that slopes obeying <math>m-1m_2=-1</math> imply perpendicular lines
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28 January 2024

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Date/TimeThumbnailDimensionsUserComment
current01:34, 29 January 2024 Thumbnail for version as of 01:34, 29 January 2024 149 ×ばつ 129 (26 KB)Guy vandegrift fixed arrows
22:15, 28 January 2024 Thumbnail for version as of 22:15, 28 January 2024 149 ×ばつ 129 (21 KB)Guy vandegrift Uploaded own work with UploadWizard

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