Find the value of m if the perpendicular bisector of the line that passes through the point (6,8) and (m,2) has slope -2.

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academicsfirst's profile pic

academicsfirst | High School Teacher | (Level 2) Adjunct Educator

Posted on

We know that the slope of the perpendicular bisector is the opposite reciprocal of the slope containing the two given points.

Therefore, the slope of the line containing the two given points is 1/2.

Using 1/2 as the slope, we use the slope formula to find the value of m.

=> slope = (difference in y values) / (difference in x values)

=> 1/2 = ( 2 - 8) / ( m - 6 )

= > m = - 6

The value of m is - 6.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll remember the fact that the product of the values of the slopes of 2 perpendicular lines is -1.

We know that the slope of perpendicular bisector is -2.

-2*a = -1, a is the slope

a = 1/2

The slope of the line that passes through points  (6,8) and (m,2) is a = 1/2.

We'll write the formula of the slope:

a = (2-8)/(m-6)

1/2 = -6/(m-6)

m-6 = -12

m = -12 + 6

k = -6

The value of the coordinate m is: m = -6.

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