High School Math : How to find the equation of a perpendicular line

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #24 : Coordinate Geometry

Write an equation in slope-intercept form for the line that passes through and that is perpendicular to a line which passes through the two points and .

Possible Answers:

Correct answer:

Explanation:

Find the slope of the line through the two points. It is .

Since the slope of a perpendicular line is the negative reciprocal of the original line, the new line's slope is . Plug the slope and one of the points into the point-slope formula  . Isolate for

 

Example Question #2 : How To Find The Equation Of A Perpendicular Line

Find the equation of a line perpendicular to 

Possible Answers:

Correct answer:

Explanation:

Since a perpendicular line has a slope that is the negative reciprocal of the original line, the new slope is . There is only one answer with the correct slope.

Example Question #3 : Perpendicular Lines

Find the equation (in slope-intercept form) of a line perpendicular to 

Possible Answers:

Correct answer:

Explanation:

First, find the slope of the original line, which is . You can do this by isolating for  so that the equation is in slope-intercept form. Once you find the slope, just replace the  in the original equation withe the negative reciprocal (perpendicular lines have a negative reciprocal slope for each other). Thus, your answer is 

Example Question #1 : How To Find The Equation Of A Perpendicular Line

Given the equation  and the point , find the equation of a line that is perpendicular to the original line and passes through the given point. 

Possible Answers:

Correct answer:

Explanation:

In order for two lines to be perpendicular, their slopes must be opposites and recipricals of each other. The first step is to find the slope of the given equation:

Therefore, the slope of the perpendicular line must be . Using the point-slope formula, we can find the equation of the new line:

Example Question #4 : How To Find The Equation Of A Perpendicular Line

What line is perpendicular to through ?

Possible Answers:

Correct answer:

Explanation:

Perdendicular lines have slopes that are opposite reciprocals.  The slope of the old line is , so the new slope is .

Plug the new slope and the given point into the slope intercept equation to calculate the intercept:

or , so .

Thus , or .

Example Question #5 : How To Find The Equation Of A Perpendicular Line

What is the equation, in slope-intercept form, of the perpendicular bisector of the line segment that connects the points  and ?

Possible Answers:

Correct answer:

Explanation:

First, calculate the slope of the line segment between the given points.

We want a line that is perpendicular to this segment and passes through its midpoint. The slope of a perpendicular line is the negative inverse. The slope of the perpendicular bisector will be .

Next, we need to find the midpoint of the segment, using the midpoint formula.

Using the midpoint and the slope, we can solve for the value of the y-intercept.

Using this value, we can write the equation for the perpendicular bisector in slope-intercept form.

Example Question #6 : How To Find The Equation Of A Perpendicular Line

What line is perpendicular to through ?

Possible Answers:

Correct answer:

Explanation:

The equation is given in the slope-intercept form, so we know the slope is .  To have perpendicular lines, the new slope must be the opposite reciprocal of the old slope, or

Then plug the new slope and the point into the slope-intercept form of the equation:

so so  

So the new equation becomes:  and in standard form

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