How to find the Location of the point P

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Discussion Overview

The discussion revolves around determining the location of a point P based on its specified distances from a straight line AB and a point A. Participants explore geometric constructions and the implications of these distances, focusing on sketching and identifying possible locations for point P.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant suggests that point P lies 5 cm away from point A, implying a diagonal length from A to P of 5 cm.
  • Another participant proposes using a compass to draw a circle with a radius of 5 cm centered at point A to find point P.
  • There is a suggestion that the intersection of the arc from point A with radius 5 cm on line CD could be point P.
  • Some participants note that there are two additional possible locations for point P on the opposite side of line AB.
  • Further, it is mentioned that extending line CD could yield another location for point P, leading to a total of four possible locations: two on line CD and two on a line parallel to AB, 3 cm away.

Areas of Agreement / Disagreement

Participants generally agree on the method of using a compass and the implications of the distances, but there is no consensus on the exact locations of point P, as multiple potential locations are identified.

Contextual Notes

The discussion does not resolve the specific geometric configurations or assumptions about the orientation of the lines and points involved.

mathlearn
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A portion of a sketch drawn by a student to obtain the location of a point P which lies at a distance of 3cm from the given straight line AB and 5cm from the point A, is shown in the figure. Complete the sketch and mark the location of the point P.

View attachment 5966

point P which lies at a distance of 3cm from the given straight line AB

This is is already included.

And the point P lies 5 cm away from point A, This should mean the diagonal length from the point A to the point P should be 5cm.

So, Any Ideas on the location of point 'P'. (Smile)
 

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mathlearn said:
A portion of a sketch drawn by a student to obtain the location of a point P which lies at a distance of 3cm from the given straight line AB and 5cm from the point A, is shown in the figure. Complete the sketch and mark the location of the point P.

This is is already included.

And the point P lies 5 cm away from P , So any Ideas on the location of point 'P'. (Smile)

Take a look at my avatar and find x? ;)

Alternatively, use a compass to draw a circle with radius 5 cm and A at its center.
 
I like Serena said:
Take a look at my avatar and find x? ;)

(Smile) (Giggle) Here It Is
I like Serena said:
Alternatively, use a compass to draw a circle with radius 5 cm and A at its center.

Hmm.. The intersection point of the arc from the point A with radius 5 cm on the line CD would be point P then?
 
mathlearn said:
(Smile) (Giggle) Here It Is

Hmm.. The intersection point of the arc from the point A with radius 5 cm on the line CD would be point P then?

Yep. (Nod)
 
I like Serena said:
Yep. (Nod)

Thank you so much ! (Smile)
 
Of course there are two other possible locations of $P$ on the other side of $AB$…
 
Evgeny.Makarov said:
Of course there are two other possible locations of $P$ on the other side of $AB$…

And if we extend the line CD there can be another location too!

So there can be four possible location for P two on CD & the other would be on a line 3 cm away & parallel to AB.

View attachment 6055

Many Thanks :)
 

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