Question

if 2x + 3y +4 = o is the perpendicular bisector of the segment joining the points A(1,2) and B(alpha,beta) ,then the value of ( alpha+ beta) is

a) -81/13
b)-136/13
c)-135/13
d)-134/13.



plz answer Quickly......it's very important....I have xam tmrw

Answer 1

dear !!!!!

perpendicular bisector means the line bisected and perpendicular upon it .
so,
2x +3y +4 =0
and A (1, 2) and B( alpha , beta )

midpoint of joining point AB is consider the in line 2x +3y +4 =0

so, {( 1+ alpha)/2 , ( 2 + beta }/2} lies in
2x +3y +4 =0

so, 2( 1+alpha)/2 +3(2+beta)/2 +4 =0

2 + 2alpha + 6 + 3beta +8 =0

2alpha +3beta + 16 =0 ------(1)

again ,

slope of AB × slope of (2x +3y+4=0) = -1
( beta -2)/( alpha-1)× -2/3 = -1

2(beta -2) = 3( alpha -1)

3alpha -3 =2beta -4

3alpha -2beta +1 =0 -------(2)

solve equations (1) and (2)

13alpha + 32 +3 =0
13alpha +35 =0
alpha = -35/13

and
2 beta = (-105 +13)/13 = -92 /13
beta = -46/13

so, alpha + beta = -81/13