Verifying Lines are Perpendicular

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SUMMARY

The discussion centers on verifying the perpendicularity of two lines, L: x - 2y + 3 = 0 and K: 2x + y = 0. The method to confirm their perpendicularity involves converting the equations to slope-intercept form (y = mx + b) and comparing their slopes. The lines are perpendicular if their slopes are negative reciprocals of each other. In this case, the slopes calculated are 2 and -1/2, confirming that the lines are indeed perpendicular.

PREREQUISITES
  • Understanding of linear equations and slope-intercept form
  • Knowledge of negative reciprocals in geometry
  • Familiarity with algebraic manipulation of equations
  • Basic skills in solving equations
NEXT STEPS
  • Learn how to convert standard form equations to slope-intercept form
  • Study the properties of perpendicular lines in coordinate geometry
  • Explore examples of verifying line relationships using slope
  • Practice problems involving the determination of line slopes
USEFUL FOR

Students studying geometry, mathematics educators, and anyone looking to strengthen their understanding of line relationships in coordinate systems.

odolwa99
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Just a quick question here. Have I done this correctly? Do I need to factor in the 3 from L?

Many thanks.

Homework Statement



Q. Verify that the lines L: x -2y + 3 = 0 & K: 2x + y = 0 are perpendicular.

Homework Equations



The Attempt at a Solution



x(x) + y(y) = 0 => 1(2) + (-2)(1) = 2 - 2 = 0.
 
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I have no idea what your solution is supposed to show, but verifying that two lines are perpendicular is easy. Just put them in y=mx+b form and compare them. If their slopes are opposite and reciprocal (2/3, -3/2 for example), then they are perpendicular.
 
Ok, thank you.
 

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