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555-605 (Medium)|   Coordinate Plane|                                 
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Kimberly77
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In the xy-coordinate plane, is point R equidistant from 04 Dec 2023, 02:27
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Bunuel
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

Look at the diagram below:



Notice, that the green line (x=-1) is the perpendicular bisector of the line segment with endpoints (-3,-3) and (1,-3), thus ANY point on this line will be equidistant from points (-3,-3) and (1,-3).

(1) The x-coordinate of point R is -1 --> point R is on the green line. Sufficient.
(2) Point R lies on the line y = -3 --> point R may or may not be on the green line. Not sufficient.

Answer: A.

Show Spoiler
Attachment:
Equidistant points.png
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Great explanation Bunuel.
One question I used midpoint formula to calculate and get (-1, -3) so arrive at answer C.
Not sure where's my thinking gone wrong?

Could you help clarify? Thanks
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In the xy-coordinate plane, is point R equidistant from 04 Dec 2023, 05:01
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Kimberly77
Bunuel
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

Look at the diagram below:



Notice, that the green line (x=-1) is the perpendicular bisector of the line segment with endpoints (-3,-3) and (1,-3), thus ANY point on this line will be equidistant from points (-3,-3) and (1,-3).

(1) The x-coordinate of point R is -1 --> point R is on the green line. Sufficient.
(2) Point R lies on the line y = -3 --> point R may or may not be on the green line. Not sufficient.

Answer: A.

Show Spoiler
Attachment:
Equidistant points.png

Great explanation Bunuel.
One question I used midpoint formula to calculate and get (-1, -3) so arrive at answer C.
Not sure where's my thinking gone wrong?

Could you help clarify? Thanks
Show more

Yes, the point (-1, -3), being the midpoint of (-3,-3) and (1,-3), is indeed equidistant from them. However, it's not necessary for point R to be exactly at (-1, -3) to be equidistant from points (-3,-3) and (1,-3). As illustrated in the diagram above, if R is located anywhere on the green line, it will be equidistant from points (-3,-3) and (1,-3). The first statement confirms that point R is on the green line, making it sufficient by itself. Therefore, we don't need the second statement to determine the answer.

Hope it's clear.
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In the xy-coordinate plane, is point R equidistant from 04 Dec 2023, 10:35
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Kimberly77
Bunuel
In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3) ?

Look at the diagram below:



Notice, that the green line (x=-1) is the perpendicular bisector of the line segment with endpoints (-3,-3) and (1,-3), thus ANY point on this line will be equidistant from points (-3,-3) and (1,-3).

(1) The x-coordinate of point R is -1 --> point R is on the green line. Sufficient.
(2) Point R lies on the line y = -3 --> point R may or may not be on the green line. Not sufficient.

Answer: A.

Show Spoiler
Attachment:
Equidistant points.png

Great explanation Bunuel.
One question I used midpoint formula to calculate and get (-1, -3) so arrive at answer C.
Not sure where's my thinking gone wrong?

Could you help clarify? Thanks

Yes, the point (-1, -3), being the midpoint of (-3,-3) and (1,-3), is indeed equidistant from them. However, it's not necessary for point R to be exactly at (-1, -3) to be equidistant from points (-3,-3) and (1,-3). As illustrated in the diagram above, if R is located anywhere on the green line, it will be equidistant from points (-3,-3) and (1,-3). The first statement confirms that point R is on the green line, making it sufficient by itself. Therefore, we don't need the second statement to determine the answer.

Hope it's clear.
Show more

Great thanks Bunuel, get it.
In other words in this type of midpoint question, does it mean as long as we know the value in X-axis is sufficient? Whereas Y-axis value is not relevant here?
Thanks
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In the xy-coordinate plane, is point R equidistant from 04 Dec 2023, 11:25
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Great thanks Bunuel, get it.
In other words in this type of midpoint question, does it mean as long as we know the value in X-axis is sufficient? Whereas Y-axis value is not relevant here?
Thanks
Show more

I recognize the inclination towards generalization and the desire to formalize everything into strict rules. Nevertheless, it's crucial to thoroughly comprehend individual cases before attempting to generalize them. In this particular question, the first statement is sufficient because it says that point R is located on a line which is perpendicular bisector of two points (-3,-3) and (1,-3). Thus, no matter where on this line point R is located, it will be equidistant from points (-3,-3) and (1,-3). As you can see, it's not about x or y-axis, rather about the specific properties of the geometry involved. In this case, the key property is that any point on the perpendicular bisector of a line segment is equidistant from the segment's endpoints. Therefore, knowing the x-coordinate is sufficient in this scenario because it places point R on that crucial perpendicular bisector. This principle, rather than a general rule about x or y values, guides the solution here.
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In the xy-coordinate plane, is point R equidistant from 04 Dec 2023, 13:47
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Kimberly77

Great thanks Bunuel, get it.
In other words in this type of midpoint question, does it mean as long as we know the value in X-axis is sufficient? Whereas Y-axis value is not relevant here?
Thanks

I recognize the inclination towards generalization and the desire to formalize everything into strict rules. Nevertheless, it's crucial to thoroughly comprehend individual cases before attempting to generalize them. In this particular question, the first statement is sufficient because it says that point R is located on a line which is perpendicular bisector of two points (-3,-3) and (1,-3). Thus, no matter where on this line point R is located, it will be equidistant from points (-3,-3) and (1,-3). As you can see, it's not about x or y-axis, rather about the specific properties of the geometry involved. In this case, the key property is that any point on the perpendicular bisector of a line segment is equidistant from the segment's endpoints. Therefore, knowing the x-coordinate is sufficient in this scenario because it places point R on that crucial perpendicular bisector. This principle, rather than a general rule about x or y values, guides the solution here.
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Noted thanks Bunuel :please: great explanation always.
Wondering that knowing x alone being sufficient here is any relation with both y coordinate is -3 here?
How about if both y coordinates are different? Will St1 still be sufficient? Thanks
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In the xy-coordinate plane, is point R equidistant from 04 Dec 2023, 14:44
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Kimberly77
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Kimberly77

Great thanks Bunuel, get it.
In other words in this type of midpoint question, does it mean as long as we know the value in X-axis is sufficient? Whereas Y-axis value is not relevant here?
Thanks

I recognize the inclination towards generalization and the desire to formalize everything into strict rules. Nevertheless, it's crucial to thoroughly comprehend individual cases before attempting to generalize them. In this particular question, the first statement is sufficient because it says that point R is located on a line which is perpendicular bisector of two points (-3,-3) and (1,-3). Thus, no matter where on this line point R is located, it will be equidistant from points (-3,-3) and (1,-3). As you can see, it's not about x or y-axis, rather about the specific properties of the geometry involved. In this case, the key property is that any point on the perpendicular bisector of a line segment is equidistant from the segment's endpoints. Therefore, knowing the x-coordinate is sufficient in this scenario because it places point R on that crucial perpendicular bisector. This principle, rather than a general rule about x or y values, guides the solution here.

Noted thanks Bunuel :please: great explanation always.
Wondering that knowing x alone being sufficient here is any relation with both y coordinate is -3 here?
How about if both y coordinates are different? Will St1 still be sufficient? Thanks
Show more

As, I said above, the first statement is sufficient because it says that point R is located on a line which is perpendicular bisector of two points (-3,-3) and (1,-3). The y-coordinates of both points being -3, means these points lie on a horizontal line. If the points were not on a horizontal line, the first statement about R being on a vertical line wouldn't necessarily indicate that R is equidistant from both points making it not sufficient.
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In the xy-coordinate plane, is point R equidistant from 05 Dec 2023, 09:28
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Get it thanks a bunch @Bunuel...you're the Legend !!!
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In the xy-coordinate plane, is point R equidistant from 24 Dec 2025, 02:10
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