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15 May 2012, 21:23
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Difficulty:
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Question Stats:
71% (01:44) correct
29%
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wrong
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In the rectangular coordinate system, the line y = x is the perpendicular bisector of segment AB (not shown), and the y-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (3; 2), what are the coordinates of point C?
A. (-3;-2)
B. (-2; 3)
C. (3;-2)
D. (2;-3)
E. (2; 3)
A. (-3;-2)
B. (-2; 3)
C. (3;-2)
D. (2;-3)
E. (2; 3)
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Capture.GIF [ 15.25 KiB | Viewed 27518 times ]
16 May 2012, 00:12
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In the rectangular coordinate system, the line y = x is the perpendicular bisector of segment AB (not shown), and the y-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (3; 2), what are the coordinates of point C?
A. (-3;-2)
B. (-2; 3)
C. (3;-2)
D. (2;-3)
E. (2; 3)
Since the line y=x is the perpendicular bisector of segment AB, then point B is the mirror reflection of point A around the line y=x, so its coordinates are (2, 3). The same way, since the y-axis is the perpendicular bisector of segment BC then the point C is the mirror reflection of point B around the y-axis, so its coordinates are (-2, 3).
Answer: B.
The question becomes much easier if you just draw a rough sketch: 
Point C.png [ 13.36 KiB | Viewed 27449 times ]
Now, you can simply see that options A, C, and D (blue dots) just cannot be the right answers. As for option E: point (2, 3) coincides with point B, so it's also not the correct answer. Only answer choice B remains.
Answer: B.
A. (-3;-2)
B. (-2; 3)
C. (3;-2)
D. (2;-3)
E. (2; 3)
Since the line y=x is the perpendicular bisector of segment AB, then point B is the mirror reflection of point A around the line y=x, so its coordinates are (2, 3). The same way, since the y-axis is the perpendicular bisector of segment BC then the point C is the mirror reflection of point B around the y-axis, so its coordinates are (-2, 3).
Answer: B.
The question becomes much easier if you just draw a rough sketch:
Attachment:
Point C.png [ 13.36 KiB | Viewed 27449 times ]
Now, you can simply see that options A, C, and D (blue dots) just cannot be the right answers. As for option E: point (2, 3) coincides with point B, so it's also not the correct answer. Only answer choice B remains.
Answer: B.
General Discussion
15 May 2012, 22:30
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Given :
1> y = x is the perpendicular bisector of segment AB
2> x = 0 (y-axis) is the perpendicular bisector of segment BC
3> If the coordinates of point A are (3, 2)
Combining 1 and 3, we can deduce that point B is the reflection of point A in the Axis Bisector (y = x)
=> Coordinates of Point B would be reverse of A and that is (2, 3)
Note : here reflection is in X=Y , so x -coordinate and y - coordinate would exchange their places.
So we can say :
4> If the coordinates of point B are (2, 3)
Combining 3 and 4, we can deduce that point C is the reflection of point B in the Y Axis (x = 0) line
=> Coordinates of Point C would be reverse of B and that is (-2, 3)
Note : here reflection is in Y axis , so sign of x -coordinate would change while sign of y coordinate would remain same.
Hope it makes sense.
1> y = x is the perpendicular bisector of segment AB
2> x = 0 (y-axis) is the perpendicular bisector of segment BC
3> If the coordinates of point A are (3, 2)
Combining 1 and 3, we can deduce that point B is the reflection of point A in the Axis Bisector (y = x)
=> Coordinates of Point B would be reverse of A and that is (2, 3)
Note : here reflection is in X=Y , so x -coordinate and y - coordinate would exchange their places.
So we can say :
4> If the coordinates of point B are (2, 3)
Combining 3 and 4, we can deduce that point C is the reflection of point B in the Y Axis (x = 0) line
=> Coordinates of Point C would be reverse of B and that is (-2, 3)
Note : here reflection is in Y axis , so sign of x -coordinate would change while sign of y coordinate would remain same.
Hope it makes sense.
