GMAT Math : Calculating the equation of a perpendicular line

Example Questions

Example Question #1 : Calculating The Equation Of A Perpendicular Line

What is the equation of the line that is perpendicular to and goes through point ?

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other.

The slope for the given line is , from  , where  is the slope. Therefore, the negative reciprocal is .

and      :

Example Question #2 : Calculating The Equation Of A Perpendicular Line

Write the equation of a line that is perpendicular to  and goes through point ?

Explanation:

A perpendicular line has a negative reciprocal slope to the given line.

The given line, , has a slope of , as is the slope in the standard form equation  .

Slope of perpendicular line:

Point:

Using the point slope formula, we can solve for the equation:

Example Question #3 : Calculating The Equation Of A Perpendicular Line

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

Explanation:

Given

We need a perpendicular line going through (14,0).

Perpendicular lines have opposite reciprocal slopes.

So we get our slope to be

Next, plug in all our knowns into  and solve for .

.

.

Example Question #4 : Calculating The Equation Of A Perpendicular Line

Given the function , which of the following is the equation of a line perpendicular to  and has a -intercept of ?

Explanation:

Given a line  defined by the equation  with slope , any line that is perpendicular to  must have a slope, or the negative reciprocal of .

Since , the slope  is  and the slope of any line  parallel to  must have a slope of .

Since  also needs to have a -intercept of , then the equation for  must be .

Example Question #5 : Calculating The Equation Of A Perpendicular Line

Given the function , which of the following is the equation of a line perpendicular to  and has a -intercept of ?

Explanation:

Given a line  defined by the equation  with slope , any line that is perpendicular to  must have a slope, or the negative reciprocal of .

Since , the slope  is  and the slope of any line  parallel to  must have a slope of .

Since  also needs to have a -intercept of , then the equation for  must be .

Example Question #6 : Calculating The Equation Of A Perpendicular Line

Given the function , which of the following is the equation of a line perpendicular to  and has a -intercept of ?

None of the above

Explanation:

Given a line  defined by the equation  with slope , any line that is perpendicular to  must have a slope, or the negative reciprocal of .

Since , the slope  is  and the slope of any line  parallel to  must have a slope of .

Since  also needs to have a -intercept of , then the equation for  must be .

Example Question #7 : Calculating The Equation Of A Perpendicular Line

Determine the equation of a line perpendicular to  at the point .