GMAT Math : Calculating whether lines are perpendicular

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #11 : Calculating Whether Lines Are Perpendicular

Which of the following lines is perpendicular to 

Possible Answers:

Not enough information provided.

Correct answer:

Explanation:

Given a line  defined by the equation  with a slope of , any line perpendicular to  would have a slope that is the negative reciprocal of , . Given our equation  , we know that  and that 

The only answer choice with this slope is 

Example Question #12 : Calculating Whether Lines Are Perpendicular

Which of the following lines is perpendicular to 

Possible Answers:

Two of the answers are correct.

Correct answer:

Two of the answers are correct.

Explanation:

Given a line  defined by the equation  with a slope of , any line perpendicular to  would have a slope that is the negative reciprocal of . Given our equation  , we know that  and that 

There are two answer choices with this slope,  and  . 

Example Question #13 : Calculating Whether Lines Are Perpendicular

A given line  is defined by the equation . Which of the following lines would be perpendicular to line ?

Possible Answers:

Not enough information provided 

Correct answer:

Explanation:

For any line  with an equation  and slope , a line that is perpendicular to  must have a slope of , or the negative reciprocal of . Given , we know that  and therefore know that 

Only one equation above has a slope of 

Example Question #14 : Calculating Whether Lines Are Perpendicular

What is the slope of a line that is perpendicular to 

Possible Answers:

Correct answer:

Explanation:

For any line  with an equation  and slope , a line that is perpendicular to  must have a slope of , or the negative reciprocal of . Given the equation , we know that  and therefore know that .

Example Question #15 : Calculating Whether Lines Are Perpendicular

Which of the following lines is perpendicular to ?

Possible Answers:

Two lines are perpendicular 

None of the lines is perpendicular

Correct answer:

Two lines are perpendicular 

Explanation:

For any line  with an equation  and slope , a line that is perpendicular to  must have a slope of , or the negative reciprocal of . Given the equation , we know that  and therefore know that 

Given a slope of , we know that there are two solutions provided:  and 

Example Question #401 : Geometry

What is the slope of a line perpendicular to that of 

Possible Answers:

Correct answer:

Explanation:

First, we need to rearrange the equation into slope-intercept form.  .

  Therefore, the slope of this line equals  Perpendicular lines have slope that are the opposite reciprocal, or 

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