All GMAT Math Resources
Example Questions
Example Question #50 :Lines
What is the equation of the line that is perpendicular toand goes through point?
Perpendicular lines have slopes that are negative reciprocals of each other.
The slope for the given line is, from, whereis the slope. Therefore, the negative reciprocal is.
and:
Example Question #1 :Calculating The Equation Of A Perpendicular Line
Write the equation of a line that is perpendicular toand goes through point?
A perpendicular line has a negative reciprocal slope to the given line.
The given line,, has a slope of, asis 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 #1 :Calculating The Equation Of A Perpendicular Line
Given, find the equation of a line that is perpendicular toand goes through the point.
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 intoand solve for.
.
Making our answer
.
Example Question #3 :Calculating The Equation Of A Perpendicular Line
Given the function,下列哪项是一条直线的方程perpendicular toand has a-intercept of?
Given a linedefined by the equationwith slope, any line that is perpendicular tomust have a slope, or the negative reciprocal of.
Since, the slopeisand the slope of any line平行于must have a slope of.
Sincealso needs to have a-intercept of, then the equation formust be.
Example Question #4 :Calculating The Equation Of A Perpendicular Line
Given the function,下列哪项是一条直线的方程perpendicular toand has a-intercept of?
Given a linedefined by the equationwith slope, any line that is perpendicular tomust have a slope, or the negative reciprocal of.
Since, the slopeisand the slope of any line平行于must have a slope of.
Sincealso needs to have a-intercept of, then the equation formust be.
Example Question #5 :Calculating The Equation Of A Perpendicular Line
Given the function,下列哪项是一条直线的方程perpendicular toand has a-intercept of?
None of the above
Given a linedefined by the equationwith slope, any line that is perpendicular tomust have a slope, or the negative reciprocal of.
Since, the slopeisand the slope of any line平行于must have a slope of.
Sincealso needs to have a-intercept of, then the equation formust be.
Example Question #6 :Calculating The Equation Of A Perpendicular Line
Determine the equation of a line perpendicular toat the point.
The equation of a line in standard form is written as follows:
Whereis the slope of the line andis the y intercept. First, we can determine the slope of the perpendicular line using the knowledge that its slope must be the negative reciprocal of the slope of the line to which it is perpendicular. For the given line, we can see that, so the slope of a line perpendicular to it will be the negative reciprocal of that value, which gives us:
Now that we know the slope of the perpendicular line, we can plug its value into the formula for a line along with the coordinates of the given point, allowing us to calculate the-intercept,:
We now have the slope and the-intercept of the perpendicular line, which is all we need to write its equation in standard form:
Example Question #1 :Calculating The Slope Of A Perpendicular Line
What is the slope of the line perpendicular to?
Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, rewrite the equation in slope intercept form:
Slope of given line:
Negative reciprocal:
Example Question #2 :Calculating The Slope Of A Perpendicular Line
Line 1 is the line of the equation. Line 2 is perpendicular to this line. What is the slope of Line 2?
Rewrite in slope-intercept form:
The slope of the line is the coefficient of, which is. A line perpendicular to this has as its slope the opposite of the reciprocal of:
Example Question #3 :Calculating The Slope Of A Perpendicular Line
Given:
Calculate the slope of, a line perpendicular to.
To find the slope of a line perpendicular to a given line, simply take the opposite reciprocal of the slope of the given line.
Since f(x) is given in slope intercept form,
.
Therefore our original slope is
So our new slope becomes: