answersLogoWhite

0


Best Answer

Not sure of an exact proof, but here's a way to think about how it works: First note that the y axis is perpendicular to the x axis. Now take a line, say y = (2/3)*x. So we can take rise/run = 2/3, and from the origin, it rises +2 and runs +3, so that the point (3,2) is on the line and connect the origin to (3,2) and you have the line.

Now if you want to rotate this line counterclockwise 90°, to get a perpendicular line. Start at the origin and now we have an x' {that's x-prime, which is in the altered coordinate system}. Note that positive x' is 90° counterclockwise from regular x-axis (x' coincides with positive regular y-axis). And positive y' coincides with negative (regular x) axis.

So the point (x',y') which in our example (3',2') will rise' 2 on the y' axis (which is really moving -2 in the regular x direction). Then it will run' 3 on the x' axis (which is really moving +3 in the regular y direction). So we have the point (-2,3) is a point on the perpendicular line. Connect this to the origin and we have the perpendicular line, and note the negative reciprocal slope.

User Avatar

Wiki User

12y ago
This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: Why does the negative reciprocal of the slope tell us your new line is perpendicular?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

If one slope is -1 what is the slope of the perpendicular slope?

The slope of the perpendicular is the negative reciprocal of the slope of a line. In this case, - (1 / -1) = 1.The slope of the perpendicular is the negative reciprocal of the slope of a line. In this case, - (1 / -1) = 1.The slope of the perpendicular is the negative reciprocal of the slope of a line. In this case, - (1 / -1) = 1.The slope of the perpendicular is the negative reciprocal of the slope of a line. In this case, - (1 / -1) = 1.


What is the formula for Perpendicular Slope?

Line a with a slope perpendicular to that of line b has a slope that is the negative reciprocal of line b's. So basically the negative reciprocal.


What is the slope of a perpendicular line is always?

The negative reciprocal of the slope of the line to which it is perpendicular.


What is the slope of a line perpendicular to line y equals -2x plus 6?

The slope of the perpendicular to a line has a slope which is the negative reciprocal of the original line's slope.The negative reciprocal of x is -1/xSo in this case, where the slope is -2 the perpendicular line has the slope -1/(-2) or simply 1/2


What is the slope of a line that is perpendicular?

If the line has a slope of 2, then the perpendicular line has a slope of -1/2. The slope of a perpendicular line is the negative reciprocal. Another example would be if the slope of a line is -1/4, then the slope of the perpendicular is 4.


Slope of a line AB is 4 what is the slope of CD if CD is perpendicular to AB?

Slope of perpendicular line is the negative reciprocal. So it is -1/4


The slopes of perpendicular lines are?

They are the negative reciprocal of each other. Fo rexample, if a line has slope = +2, then the line perpendicular to it has slope -1/2


Do perpendicular lines have the same exact slope?

No, parallel lines have exactly same slope Perpendicular line have a slope that is negative reciprocal of each other that is if m = slope of line then slope of perpendicular line is -1/m


How do you write the equation for a perpendicular line?

Take the negative reciprocal of the lines slope you want it to be perpendicular to. For example y = 3x +2; perpendicular line slope is -1/3.


What is the slope of a line that is peroendicular to the line y equals 2x plus 5?

Perpendicular lines have a negative reciprocal slope. Slope of y=2x+5 is 2/1 negative reciprocal is (-1/2)


The slope of line a is 3 what is the slope of a line perpendicular to a?

To find the slope of a perpendicular line, take the negative reciprocal of the slope of the given line. (Flip the top and bottom of the fraction and change the sign.) The slope of 3 can be written as 3/1. The slope of a line that is perpendicular is -1/3.


What is the slope of the perpendicular to the line whose equation is y equals 5x-7?

12