Write The Equation Of Perpendicular Line Worksheet

6 problems

Find the negative reciprocal of the original line's slope in order to obtain the equation of a perpendicular line to a given line. The perpendicular line will have a slope of `-\frac{1}{m}` if the slope of the original line is \( m \). Next, substitute the slope and a point where the perpendicular line passes in the point-slope form of a line equation \( y - y_1 = m(x - x_1) \).

Algebra 1
Linear Relationship

How Will This Worksheet on "Write the Equation of Perpendicular Line" Benefit Your Student's Learning?

  • Reinforces the concept that slopes of perpendicular lines are negative reciprocals.
  • Enhances problem-solving abilities by applying mathematical theory to practical issues.
  • Prepares students for advanced math classes like calculus and geometry.
  • Essential for professions requiring precise angles, such as engineering and architecture.
  • Encourages critical thinking and the study of geometric relationships.
  • Improves communication skills in expressing mathematical ideas clearly.
  • Builds confidence in solving challenging mathematical tasks.

How to Write the Equation of Perpendicular Line?

  • Determine the equation of the given line in
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Solved Example

Q. Line gg has an equation of y=2x+1y = 2x + 1. Line hh includes the point (5,2)(-5,2) and is perpendicular to line gg. What is the equation of line hh?\newlineWrite the equation in slope-intercept form.
  1. Perpendicular Lines Slopes: Line hh is perpendicular to line gg.\newlineAre their slopes the same or opposite reciprocals?\newlineSlopes of perpendicular lines are opposite reciprocals.
  2. Equation of Line g: Equation of line g: \newliney=2x+1y = 2x + 1\newlineFind the slope of line g.\newlineCompare y=2x+1y = 2x + 1 with y=mx+by = mx + b.\newlinem=2m = 2\newlineSlope of line g: 22
  3. Slope of Line hh: Line hh is perpendicular to gg.\newlineSlope of line gg: 22\newlineFind the slope of line hh.\newlineOpposite reciprocal of 22 is 12-\frac{1}{2}.\newlineSlope of line hh: 12-\frac{1}{2}
  4. Y-Intercept Calculation: For line hh: \newlineSlope (mm): 12-\frac{1}{2} \newlinePoint: (5,2)(-5, 2) \newlinePlug these values in y=mx+by = mx + b and find the y-intercept.\newline2=12(5)+b2 = -\frac{1}{2}(-5) + b \newline2=52+b2 = \frac{5}{2} + b\newline252=b2 - \frac{5}{2} = b\newline4252=b\frac{4}{2} - \frac{5}{2} = b\newline12=b-\frac{1}{2} = b
  5. Equation of Line h: For line h: \newlineSlope mm: 12-\frac{1}{2} \newliney-intercept bb: 12-\frac{1}{2} \newlineWhat is the equation of the line h in slope-intercept form?\newlineSubstitute 12-\frac{1}{2} for mm and 12-\frac{1}{2} for bb in y=mx+by = mx + b. \newliney = 12x12-\frac{1}{2}x - \frac{1}{2}

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