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

2 Answers
Kevin · Shantelle
May 11, 2018

11 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)y2−y1x2−x1.

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 11.

Camilleon
May 11, 2018

y = -1x + 0y=−1x+0; the reciprocal is y = 1x + 0y=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)Y2−Y1X2−X1 = mm, the slope

Label your ordered pairs:

(0, 0) (X_1, Y_1)(X1,Y1)
(-1, 1) (X_2, Y_2)(X2,Y2)

Now, plug-in your data:

(1 - 0)/(-1 - 0)1−0−1−0 = mm

Simplify.

(1)/(-1)1−1 = mm

m = -1−1 , 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−y1=m(x−x1)

y - 0 = -1(x - 0)y−0=−1(x−0)

Distribute:

y - 0 = -1x + 0y−0=−1x+0

Add zero to both sides:

y = -1x + 0y=−1x+0

If mm = 1/-11−1, the negative reciprocal will be 1/111, which makes mm 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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