Rectangular Coordinate
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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.
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.
Last edited by raghavsarathy on Tue Jul 21, 2009 4:45 pm, edited 2 times in total.
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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)
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)