Question

The equation of LINE which bisect the line joining two points (2 - 19) and( 6, 1 )and perpendicular to the line joining two points (- 1,3 )and (5, - 1) is

Answer 1

What is the equation of the perpendicular bisector of the segment joining points A (2, −2) and B (6, 4)?







Since the required line bisects the line joining (2,-2) and (6,4), it will pass through mid-point of the segment joining two points which is {(2+6)/2,(-2+4)/2} = (4,1).

Also, since the required line in perpendicular to the line joining (2,-2) and (6,4), slope (m) of the required line is given by
m = -1/(slope of line through the two points) = -(6-2)/[4-(-2)] = -2/3.

Equation of a line is given by y = mx + c.

Since the perpendicular bisector passes through (4,1) and m = -2/3, we have

1 = (-2/3)(4) + c = -8/3 + c    => c = 11/3.

Thus the equation of perpendicular bisector is given by

y = (-2/3)x + 11/3 i.e. 2x + 3y = 11.
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