Find the slope of a line perpendicular to a slope of a line is 1/3

tashiiexb0o5c

tashiiexb0o5c

Answered question

2022-09-09

Find the slope of a line perpendicular to a slope of a line is 1/3

Answer & Explanation

Savanah Morton

Savanah Morton

Beginner2022-09-10Added 15 answers

In general, if the slope of a line is m, then the slope of any perpendicular line will be - 1 m . So in your case the slope of any perpendicular line would be - 1 1 3 = - 3
To see that, consider a line given by
y=mx+c
If you reflect that line in the line y=x, you get a line whose equation is the same, but with x and y swapped:
x=my+c
If you then reflect that line in the x axis, you are basically reversing the sign of the y coordinate, so you get a line with equation:
x=−my+c
The total result of these two geometric operations is to rotate the original line through a right angle (try it yourself with a square of paper).
Now we can rearrange this new line's equation into slope intercept form as follows:
Add my to both sides:
my+x=c
Subtract x from both sides:
my=−x+c
Divide both sides by m:
y = ( - 1 m ) x + c m
Notice the new slope is - 1 m

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