What is the slope of any line perpendicular to the line passing through #(0,0)# and #(-1,1)#?

2 Answers
Kevin · Shantelle
May 11, 2018

#1# is the slope of any line perpendicular to the line

Explanation:

The slope is rise over run, #(y_2 -y_1)/(x_2-x_1)#.

The slope perpendicular to any line is it’s negative reciprocal. The slope of that line is negative one so the perpendicular to it would be #1#.

Camilleon
May 11, 2018

#y = -1x + 0#; the reciprocal is #y = 1x + 0#

Explanation:

First, we need to find the slope of the line that passes through these two points, then, we can find its reciprocal (opposite, which is perpendicular). Here's the formula for finding a slope with two points:

#(Y_2 - Y_1)/(X_2 - X_1)# = #m#, the slope

Label your ordered pairs:

(0, 0) #(X_1, Y_1)#
(-1, 1) #(X_2, Y_2)#

Now, plug-in your data:

#(1 - 0)/(-1 - 0)# = #m#

Simplify.

#(1)/(-1)# = #m#

m = #-1# , because 1 negative and 1 positive divide into a negative.

Now, let's find its equation by using the point-slope formula:

#y - y_1 = m(x - x_1)#

#y - 0 = -1(x - 0)#

Distribute:

#y - 0 = -1x + 0#

Add zero to both sides:

#y = -1x + 0#

If #m# = #1/-1#, the negative reciprocal will be #1/1#, which makes #m# change to 1.

Credit to Shantelle for correcting an error
https://www.mathsisfun.com/reciprocal.html
https://www.mathsisfun.com/definitions/reciprocal.html
http://www.purplemath.com/modules/strtlneq2.htm

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