Find Equation of line AB, is A(2,4) and B(1,3). Then find the equation of perpendicular to line segment AB

Question

Find Equation of line AB, is A(2,4) and B(1,3). Then find the equation of perpendicular to line segment AB

Answer 1

Find equation of the line through the points A and B:

 

Slope of AB  = (3 - 4)/(1 - 2) = 1

 

Equation of AB:  y - 4 = 1(x - 2)    So, y = x + 2

 

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Are you looking for the equation of the perpendicular bisector of AB?

 

If so, the perpendicular bisector passes through the midpoint of AB.

 

Midpoint of AB = ((2 + 1)/2, (4 + 3)/2) = (3/2, 7/2)

 

Since the slope of AB is 1, the slope of the perpendicular bisector is the negative reciprocal of 1, so the slope of perpendicular bisector = -1

 

Perpendicular bisector has slope -1 and goes through the point (3/2, 7/2).

 

Equation of perpendicular bisector:  y - 7/2 = -1(x - 3/2)

                                       

                                                      y - 7/2 = -x + 3/2

 

                                                             y = -x + 5