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Write the equation of the perpendicular bisector of the line AB given: (a(3,-3) & B(1,-1)

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Answer:

y = x -4

Explanation:

A perpendicular bisector of a line AB will pass through the midpoint of the line AB

AB is a line segment between A(3, -3) and B(1, -1)

Midpoint of AB is the average of the x and y coordinates of A and B

Let M be the midpoint

x coordinate of M = (3 + 1)/2 = 4/2 = 2

y coordinate of M = (-3 + (-1))/2 = -4/2 = -2

So M is at point (2, -2)

The slope of line AB can be determined as follows

Slope = (yb - ya)/(xb-xa) where (xa, ya) and (xb, yb) are coordinates of points A and B respectively

Slope of AB = (-1 - (-3)/(1 -3 = (-1 + 3) /(1 -3 ) = 2/-2 = -1

A line which is perpendicular to AB will have slope which is negative of the reciprocal of slope of AB

Slope of AB = -1
Reciprocal of slope AB = 1/-1 = -1

Negative of this reciprocal = 1

So perpendicular line will be of the form
y = 1x + b where b is the y intercept

Since this is a perpendicular bisector it has to pass through M(2, -2)

Substitute y = -2 and x = 2 to solve for b

-2 = 1(2) + b

-2 = 2 + b

-4 = b

b = -4

So the equation of the perpendicular bisector is y = x -4

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