Where is Bisector Valley? Uncovering Its Location

  • Context: MHB 
  • Thread starter Thread starter Ilikebugs
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Discussion Overview

The discussion centers around determining the location of Bisector Valley using coordinate geometry. Participants explore the mathematical approach to find the intersection of two lines that represent different legs of a journey.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant asks how to determine the location of Bisector Valley.
  • Another participant describes the first leg of a journey along a line with a slope of -1, suggesting the use of the point-slope formula to find the line.
  • The second leg of the journey is described as passing through the point (0,4) with a slope of 1, prompting a request to determine this line as well.
  • Participants calculate the intersection of the two lines, arriving at coordinates (-2, 2) for Bisector Valley.
  • There is a mention of a distance calculation involving the points (0,0), (-2,2), and (0,4), but the context and correctness of this calculation are not fully explored.

Areas of Agreement / Disagreement

Participants appear to agree on the mathematical approach to finding the intersection of the lines, but there is no explicit consensus on the implications of the distance calculation or the overall significance of the findings.

Contextual Notes

The discussion does not clarify the assumptions behind the distance calculation or the relevance of the coordinates found. There may be additional methods to determine the location of Bisector Valley that are not discussed.

Ilikebugs
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View attachment 6568 Is there a way to determine where Bisector Valley is?
 

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The first leg of Ima's journey lies along the line passing through the origin, with slope -1...so using the point-slope formula can you determine the line.

The second leg of her journey lies along the line passing through the point (0,4) and has a slope of 1...can you determine this line?

Now, find where the two lines intersect to get the coordinates of Bisector Valley. :)

Note: There are simpler ways to determine the answer to this question, but since coordinate geometry was mentioned, I felt it more appropriate to use it to work the problem. :D
 
The line of the first leg is y=-x
The line of the 2nd leg is y=x+4

-x=x+4

x= -2
y=2

Points= 0,0 -2,2 0,4

2 sqr(2)+2 sqr(2)+4= 4+4 sqr(2) km?
 
Ilikebugs said:
The line of the first leg is y=-x
The line of the 2nd leg is y=x+4

-x=x+4

x= -2
y=2

Points= 0,0 -2,2 0,4

2 sqr(2)+2 sqr(2)+4= 4+4 sqr(2) km?

Looks good to me. (Yes)
 

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