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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 90Â°, 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 90Â° 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.

Q: Why does the negative reciprocal of the slope tell us your new line is perpendicular?

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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.

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

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

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

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.

Related questions

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.

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.

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

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

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

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

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

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.

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

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.

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