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# In the xy-coordinate plane, is point R equidistant from

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In the xy-coordinate plane, is point R equidistant from [#permalink]
Kimberly77 wrote:
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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Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
Bunuel wrote:
Kimberly77 wrote:
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 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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Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
Kimberly77 wrote:
Bunuel wrote:
Kimberly77 wrote:
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 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

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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Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
Get it thanks a bunch @Bunuel...you're the Legend !!!
Re: In the xy-coordinate plane, is point R equidistant from [#permalink]
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