Question

Triangle ABC has been rotated 90° to create triangle DEF. Using the image below, prove that perpendicular lines have opposite and reciprocal slopes.

Answer 1

Given that triangle DEF is formed from triangle ABC rotated 90 degrees, this must mean that EF is perpendicular (oriented at 90 degrees) to BC.

From the diagram, we have:
Slope of EF = [-1-(-4)]/(2-5) = -1
Slope of BC = (5-2)/(4-1) = 1
Hence, the slope of BC is the negative reciprocal of the slope of EF.

Answer 2

Thank you (: I got the same answer (:

Answer 3

@jessica_leon93 : You're welcome.