State the Equation of the perpendicular bisector of segment AB with coordinates A(4,6), and B(-4, 2)

Answer 1

A( 4 , 6 ) , B( -4 , 2 )

(x1,y1) , (x2,y2)

First find slope(m) from the given points => m = (y2 - y1) / (x2 - x1)

= (2-6) / (-4-4)

= -4 / -8

= 1/2

Given the line is perpendicular

Let's say m1, m2 are the slopes of the two lines

When two lines are perpendicular,(the product of slopes), m1 * m2 = -1

m1 * m2 = -1

1 /2 * m2 = -1 { Since, m1= 1/2 }

m2 = -2

Given the line is perpendicular bisector : means the line bisects the line formed by the points A(4,6), B(-4,2)

To get the point where it bisects : Find the mid - point (Since, if a line bisects another line, that means it divides the line into two equal parts).

Let's say C divides the line.

So, to find the mid-point : ((x1 + x2)/2 , (y1+y2)/2)

A( 4 , 6 ) , B( -4 , 2 )

(x1,y1) , (x2,y2)

C = (4-4) /2 , (6+2) /2

C = (0,4)

So, now we have slope of the line and the point it passes through.

We can find the equation of the line by point slope form : (y-y1)= m(x-x1)

C = ( 0 , 4 ), m2 = -2

(x1,y1)

(y-4) = -2 (x-0)

y = -2x

2x + y = 0

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