IMO E
OA?

IMO - B [Edit my post.. Initially typo C]

Since y=x is the perpendicular bisector of AB and A lies in the first quadrant => B lies in the first quadrant.

We are also told that y axis is the perpendicular bisector of BC. Hence C must lie in the second quadrant.

i.e X negative and y positive.

Choose the answer option that satisfies this.

I am not able to solve this mathematically.. Could someone help.

thats y its has to be B and not C

Raghavsarathy, thats right. Even I got the answer. But couldn't solve it mathematically. I need help to solve it mathematically.

Well Mathematically thats what u can do..

1) You knwo line y = x is perpendicular bisector of segment AB and A is (3,2) ===> The segment AB could be of form y = -x + c , since perpendicular bisector is perpendicular to AB ..now get the line eauqntion for AB as 2 = -3 + c which gives c = 5 , hence segment AB is y = 5 - x

2) Now take out the co-ordinate where AB and perpendicular bisector insecxts , which u cna easily get using 2 eqns y = x and y = 5 - x
You get co-rdinates of points of intersection as (2.5,2.5)
Since perpendicular bisector bisects ( or divides exactly in half) the segment AB , so you know easily B is ( 2, 3)

3) Now coming to BC segment where its said y axis is the perpendicular bisector , which means BC is parallel to x axis . The midpoint of BC lies on Y axis which is nothing but (0 , 3) since segemnt BC is parallel to x axis.
Now you can derive the co-ordinates for C similaryly as you derived for B in step 2 . This gives C a (-2,3)

rohan_vus, Thanks for the explanation.