Questions: How Far from Point P is a Given Line?

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Homework Help Overview

The problem involves determining the number of points that are a specific distance from a given line and also a specific distance from a point P. The context is geometric in nature, focusing on distances and intersections in a two-dimensional space.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants suggest visualizing the problem by drawing the line and point P, and considering the loci of points at fixed distances from both the line and the point. There is discussion about the number of intersection points that satisfy the given conditions.

Discussion Status

There is an active exploration of the problem with varying interpretations of the number of points that meet the criteria. Some participants express differing views on the correct answer, indicating a lack of consensus but a productive dialogue regarding the reasoning behind their answers.

Contextual Notes

Participants are working within the constraints of a homework problem, which may limit the information available for solving the question. There is also a focus on understanding the geometric relationships involved.

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Homework Statement



A given point P is seven units from a given straight line. The number of points that are 3 units from the line and also 10 units from point P is: 1, 2, 3, or 4?

The Attempt at a Solution



Not sure how to approach this problem.
 
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Maybe you can draw it? Draw the line l and the point P.
What does the locus of all points with fixed distance to the line look like?
And all the points with fixed distance to the point?

Now find the intersects.
 
4, is this correct?
 
golb0016 said:
4, is this correct?
That's not what I would get but I may be interpreting the question differently than you. How did you get 4?
 
Actually I think it should be three. Two points to the side of the main point and one straight across.
 
Yes that's what I'm getting as well.
 

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