Find the slope of the line that is perpendicular to the line that passes through the points (1,3) and (2,6)?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The slope of two perpendicular lines m1 and m2 are related as m1* m2 = -1.

The slope of the line through (1,3) and ( 2,6) is :

m = (6 - 3)/(2 - 1)

=> m = 3

A line perpendicular to this line has a slope -1/3.

The slope of the required line is -1/3.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We know that 2 line are perpendicular if and only if the product of the values of their slopes is -1.

We can find the slope of the line that passes through the given points.

m1 = (y2 - y1)/(x2 - x1)

m1 = (6-3)/(2-1)

m1 = 3/1

m1 = 3

The product of the slopes is:

m1*m2 = -1

-3*m2 = -1

We'll divide by -3:

m2 = 1/3

The slope of the perpendicular line to the line that passes through the points (1,3) and (2,6) is m2 = 1/3.

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