MHB Where is Bisector Valley? Uncovering Its Location

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Bisector Valley's location can be determined through coordinate geometry by analyzing two lines. The first leg of the journey follows the line y = -x, while the second leg follows y = x + 4. The intersection of these two lines occurs at the coordinates (-2, 2). The calculations confirm that the distance from the origin to this point involves a combination of square roots, resulting in a total distance of 4 + 4√2 km. The solution effectively demonstrates the process of finding the intersection using the point-slope formula.
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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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