Perpendicularity Math Example 3

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Example 3

easy
Line mm passes through (0,−1)(0, -1) with slope 35\dfrac{3}{5}. Write the equation of the line perpendicular to mm through the origin.

Solution

  1. 1
    Step 1: Perpendicular slope: m⊥=−53m_\perp = -\dfrac{5}{3}.
  2. 2
    Step 2: Line through origin: y=−53xy = -\dfrac{5}{3}x.

Answer

y=−53xy = -\dfrac{5}{3}x
The negative reciprocal of 35\tfrac{3}{5} is −53-\tfrac{5}{3}. Since the line passes through the origin the yy-intercept is 00, giving the slope-intercept equation directly.

About Perpendicularity

Lines, segments, or planes that intersect at exactly a right angle of 90°90° to each other.

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More Perpendicularity Examples

Example 1 easy

Line [formula]. Write the equation of a line [formula] perpendicular to [formula] that passes throug

Example 2 medium

Determine whether triangle [formula], [formula], [formula] is a right triangle, and if so identify t

Example 4 hard

Find the foot of the perpendicular from point [formula] to the line [formula].

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