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In the rectangular coordinate below the line Y=X, is the [#permalink]
23 May 2004, 04:22

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Difficulty:

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In the rectangular coordinate below the line Y=X, is the perpendicular bisector of segment AB (Not Shown), and X axis is the oerpendicular bisector of segment BC (Not Shown). If coordinates point A are (2,3), what are the coordinate points of C?

PS: this is an OG question. Does anybody know where can I download a PDF version of OG? that way I don't have to draw all this diagram?

PDF version of OG to be downloaded - now that is scary

Actually, at least the verbal portion has been illegally scanned and was available for download on some Chinese sites. sorry, I have lost the links, but in any case, a legal copy is NOT available.

In the rectangular coordinate below the line Y=X, is the perpendicular bisector of segment AB (Not Shown), and X axis is the oerpendicular bisector of segment BC (Not Shown). If coordinates point A are (2,3), what are the coordinate points of C?

PS: this is an OG question. Does anybody know where can I download a PDF version of OG? that way I don't have to draw all this diagram?

If I understand it correctly:

the reflection of point A(2,3) in life x=y, will give us B(3,2) and further reflection of B(3,2) in y=0 (x-axis) shall give us C(3,-2).

Though have lost my touch with Coordinate Geometry, this is how brain is working right now.

In the rectangular coordinate below the line Y=X, is the perpendicular bisector of segment AB (Not Shown), and X axis is the oerpendicular bisector of segment BC (Not Shown). If coordinates point A are (2,3), what are the coordinate points of C?

PS: this is an OG question. Does anybody know where can I download a PDF version of OG? that way I don't have to draw all this diagram?

Ans (3,-2)

equation of orig line y=x
assume eq of line AB perp to y=x as y=mx+c
as this line is perp its slope will be -1 and plugging pt A(2,3) we can find eq of AB as y=-x+5
Intersection pt of AB and y=x is (2.5,2.5) and by symmetry we can say B is (3,2)
C is on the other side of B and equdistant from X axis
hence C is (3,-2)

In the rectangular coordinate below the line Y=X, is the perpendicular bisector of segment AB (Not Shown), and X axis is the oerpendicular bisector of segment BC (Not Shown). If coordinates point A are (2,3), what are the coordinate points of C?

PS: this is an OG question. Does anybody know where can I download a PDF version of OG? that way I don't have to draw all this diagram?

Ans (3,-2)

equation of orig line y=x
assume eq of line AB perp to y=x as y=mx+c
as this line is perp its slope will be -1 and plugging pt A(2,3) we can find eq of AB as y=-x+5
Intersection pt of AB and y=x is (2.5,2.5) and by symmetry we can say B is (3,2)
C is on the other side of B and equdistant from X axis
hence C is (3,-2)