# GMAT Math : Calculating whether lines are perpendicular

## Example Questions

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### Example Question #11 : Calculating Whether Lines Are Perpendicular

Which of the following lines is perpendicular to    Not enough information provided.  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   Two of the answers are correct.  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 ?   Not enough information provided  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       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 ? None of the lines is perpendicular Two lines are perpendicular 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 #16 : Calculating Whether Lines Are Perpendicular

What is the slope of a line perpendicular to that of       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 2 Next →

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