Question

10. Find the equation of the perpendicular bisector of the straight line segment joining the
points (3, 4) and (-1, 2)

Answer 1

1 ) Let A( 3 , 4 ) and B( -1 , 2 )

L is the perpendicular bisectors of AB .

L bisects AB at P .

coordinates of the point P = midpoint of AB

= ( x1 + x2/2 , y1 + y2/2 )

= ( 3 -1 /2 , 4 + 2/2 )

= ( 2/2 , 6/2 )

P = ( 1 , 3 )

2 ) slope ( m1 ) of a line A( x1 , y1 ) = ( 3 , 4 )

and B( x2 , y2 ) = ( -1 , 2 )

m1 = ( y2 - y1 )/( x2 - x1 )

= ( 2 - 4 )/( -1 - 3 )

= ( -2 )/( -4 )

m1 = 1/2

Slope( m2) of a line

perpendicular to AB =(-1/m1)

m2 = -2

Therefore ,

equation of a line whose slope ( m2 ) = -2 ,

and passing through the point P( x1, y1 ) = ( 1,3)

y - y1 = m2 ( x - x1 )

y - 3 = ( - 2 ) ( x - 1 )

y - 3 = -2x + 2

2x + y = 2 + 3

2x + y = 5

I hope this helps you.

: )