# What is the equation of the perpendicular bisector of the line joining the points (3,2) and (10,4)

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justaguide | Certified Educator

The equation of the perpendicular bisector of the line segment joining the points (3,2) and (10,4) has to be determined.

The slope of a line joining the points (3,2) and (10,4) is (4 - 2)/(10 - 3) = 2/7. As the product of the slope of perpendicular lines is equal to -1, the slope of the required bisector is -7/2.

This line passes through the a point lying exactly between the points (3,2) and (10,4) on the line joining them. The coordinates of this point are ((3+10)/2, (2+4)/2) or (13/2, 3)

A line with slope -7/2 passing through (13/2, 3) has equation (y - 3)/(x - 13/2) = -7/2

=> y - 3 = -3.5x + 22.75

=> 3.5x + y - 25.75 = 0

**The equation of the required perpendicular bisector is 3.5x + y - 25.75 = 0**