GMAT Math : Calculating whether lines are perpendicular

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Example Questions

Example Question #11 : Lines

Which of the following lines is perpendicular to $y=\frac{3}{4}x+16$ ?

Possible Answers:

$y=-\frac{4}{3}x+12$

$y=\frac{3}{4}x+7$

$y=\frac{4}{3}x+8$

Not enough information provided.

$y=\frac{3}{4}x-6$

Correct answer:

$y=-\frac{4}{3}x+12$

Explanation:

Given a line defined by the equation y=mx+b with a slope of , any line perpendicular to would have a slope that is the negative reciprocal of , $-\frac{1}{m}$ . Given our equation $y=\frac{3}{4}x+16$ , we know that $m=\frac{3}{4}$ and that $-\frac{1}{m}=-\frac{1}{\frac{3}{4}}=-\frac{4}{3}$ .

The only answer choice with this slope is $y=-\frac{4}{3}x+12$ .

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Example Question #12 : Lines

Which of the following lines is perpendicular to y=5x-12

Possible Answers:

$y=-\frac{1}{5}x+7$

$y=-\frac{1}{5}x-4$

$y=\frac{1}{5}x-6$

Two of the answers are correct.

$y=\frac{1}{5}x+19$

Correct answer:

Two of the answers are correct.

Explanation:

Given a line defined by the equation y=mx+b with a slope of , any line perpendicular to would have a slope that is the negative reciprocal of , $-\frac{1}{m}$ . Given our equation y=5x-12 , we know that m=5 and that $-\frac{1}{m}=-\frac{1}{5}$ .

There are two answer choices with this slope, $y=-\frac{1}{5}x-4$ and $y=-\frac{1}{5}x+7$ .

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Example Question #13 : Lines

A given line is defined by the equation y=2x+5 . Which of the following lines would be perpendicular to line ?

Possible Answers:

$y=-\frac{1}{2}x+7$

y=2x+14

y=-2x+7

Not enough information provided

$y=\frac{1}{2}x+7$

Correct answer:

$y=-\frac{1}{2}x+7$

Explanation:

For any line with an equation y=mx+b and slope , a line that is perpendicular to must have a slope of $-\frac{1}{m}$ , or the negative reciprocal of . Given y=2x+5 , we know that m=2 and therefore know that $-\frac{1}{m}=-\frac{1}{2}$ .

Only one equation above has a slope of $-\frac{1}{2}$ : $y=-\frac{1}{2}x+7$ .

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Example Question #14 : Lines

What is the slope of a line that is perpendicular to $y=-\frac{1}{7}x+9$

Possible Answers:

$\frac{1}{9}$

$-\frac{1}{9}$

Correct answer:

Explanation:

For any line with an equation y=mx+b and slope , a line that is perpendicular to must have a slope of $-\frac{1}{m}$ , or the negative reciprocal of . Given the equation $y=-\frac{1}{7}x+9$ , we know that $m=-\frac{1}{7}$ and therefore know that $-\frac{1}{m}=-\frac{1}{-\frac{1}{7}}=7$ .

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Example Question #15 : Lines

Which of the following lines is perpendicular to y=4x+8 ?

Possible Answers:

$y=4x-\frac{1}{8}$

$y=-\frac{1}{4}x+5$

None of the lines is perpendicular

Two lines are perpendicular

$y=-\frac{1}{4}x-4$

Correct answer:

Two lines are perpendicular

Explanation:

For any line with an equation y=mx+b and slope , a line that is perpendicular to must have a slope of $-\frac{1}{m}$ , or the negative reciprocal of . Given the equation y=4x+8 , we know that m=4 and therefore know that $-\frac{1}{m}=-\frac{1}{4}$ .

Given a slope of $-\frac{1}{4}$ , we know that there are two solutions provided: $y=-\frac{1}{4}x+5$ and $y=-\frac{1}{4}x-4$ .

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Example Question #16 : Calculating Whether Lines Are Perpendicular

What is the slope of a line perpendicular to that of 6y-3x=2?

Possible Answers:

$\frac{-1}{2}$

$\frac{1]}{2}$

Correct answer:

Explanation:

First, we need to rearrange the equation into slope-intercept form. y=mx+b .

$6y-3x=2->y=\frac{3x+2}{6}.$ Therefore, the slope of this line equals $\frac{1}{2}.$ Perpendicular lines have slope that are the opposite reciprocal, or -2.

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GMAT Math : Calculating whether lines are perpendicular

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #11 : Lines

Example Question #12 : Lines

Example Question #13 : Lines

Example Question #14 : Lines

Example Question #15 : Lines

Example Question #16 : Calculating Whether Lines Are Perpendicular

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