Parallel and Perpendicular Math Example 4

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Example 4

medium
Line ℓ\ell passes through (0,3)(0,3) and (6,0)(6,0). Find the equation of the line perpendicular to ℓ\ell passing through the origin.

Solution

  1. 1
    Slope of ℓ\ell: m1=0−36−0=−12m_1 = \dfrac{0-3}{6-0} = -\dfrac{1}{2}.
  2. 2
    Perpendicular slope: m2=−1m1=2m_2 = -\dfrac{1}{m_1} = 2.
  3. 3
    Line through origin with slope 22: y=2xy = 2x.

Answer

y=2xy = 2x
First find the slope of the given line from two points, then take its negative reciprocal for the perpendicular slope. A line through the origin has yy-intercept zero, so the equation is simply y=mxy = mx.

About Parallel and Perpendicular

Parallel lines never intersect and have matching direction; perpendicular lines intersect at right angles.

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More Parallel and Perpendicular Examples

Example 1 easy

Find the equation of the line through [formula] that is parallel to [formula].

Example 2 medium

Find the equation of the line through [formula] that is perpendicular to [formula].

Example 3 easy

Are the lines [formula] and [formula] parallel, perpendicular, or neither?

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