Coordinate problm

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jogi1984: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Wed Mar 30, 2011 7:36 am

by jogi1984 » Sun Sep 11, 2011 7:29 am

Give mirror image of (-3,2) across X=Y line ???

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Source: Beat The GMAT — Problem Solving | Sun Sep 11, 2011 7:29 am

gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 amFollowed by: 2 members; Thanked: 29 times

by gmatclubmember » Sun Sep 11, 2011 8:05 am

jogi1984 wrote:Give mirror image of (-3,2) across X=Y line ???

I guess the answer is (2,-3). But I calculated it using 2 equations in x and y variables which took me almost like 2 mins. Someone can please come up with a short cut? What if the mirror is not line x=y but ax+by+c=0.

Cheers
Ami/-

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ravirajsitaram: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sun Sep 11, 2011 2:39 am

by ravirajsitaram » Sun Sep 11, 2011 8:53 am

Straight line -- ax+by+c = 0
point (x1,y1)

To find mirror image point :
A straight line with x=x1, touches the line ax+by+c at point (x1,(-c-ax1)/b)
similarly line y=y1 touches the line at ((-c-by1)/a,y1).
Now the mirror image of (x1,y1) will be equidistant wrt line in ((-c-by1)/a,(-c-ax1)/b).

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mehrasa: Master | Next Rank: 500 Posts; Posts: 279; Joined: Fri Nov 05, 2010 5:43 pmFollowed by: 1 member; Thanked: 15 times

by mehrasa » Sun Sep 11, 2011 8:55 am

I prefer to explain 3 different situation under this topic

when we want to find reflected point based on y=x we just change the position of x-coordinate and y-coordinate (e.g. (2,3) --> (3,2))
as for x-axis => the x-coordinate will not change while y-coordinate sign reverse (e.g (3.2) --> (3,-2)
as for y-axis ==> the y-coordinate remain the same and x-coordinate sign change (3,2) --> (-3,2)

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Sun Sep 11, 2011 9:07 am

Slope of y=x is 1. The mirror image of (-3,2) along the y axis it is (3,2). Along the x-axis it is (-3,-2)

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