How do I find the equidistant point?

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    equidistant Point
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Homework Help Overview

The problem involves finding the coordinates of a point on the line defined by the equation y=3x+1 that is equidistant from the points (0,0) and (-3,4). The context is within the subject area of precalculus, specifically dealing with distance formulas and linear equations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss using the distance formula to equate distances from a point on the line to the two given points. Some express confusion about the steps involved, while others seek clarification on how to approach the problem.

Discussion Status

The discussion includes attempts to clarify the problem setup and the necessary steps to find the solution. Some participants have provided guidance on how to set up the equations based on the distance formula, while others have noted the need for more initial work from the original poster.

Contextual Notes

There is a reminder about the requirement to show work before receiving help, as indicated by the forum's homework posting guidelines. Additionally, a participant points out that the problem may not belong in the calculus category, suggesting it is more appropriate for precalculus.

BankaiNinja
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1. Find the coordinates of the point on the line y=3x+1 that is equidistant from (0,0) and (-3,4)



2. distance formula



3. I have no idea how to do this. X_X
 
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does anyone know?
 
nobody?
 
Any point on the line has coordinates (x,3x+1). Set the distance from that to (0,0) equal to the distance from that to (-3,4)
 
huh? can u show me? step by step
 
The distance between a point (x,y) and the point (-3,4) is [tex]d1=\sqrt{(x+3)^2 + (y-4)^2}[/tex]. The distance between a point (x,y) and the point (0,0) is [tex]d2 = \sqrt{x^2 + y^2}[/tex]. You know what y is from the equation of the line, so substitute that, set d1=d2, and solve for x.
 
In future, please note that you must show some work before help can be provided-- hence the presence of #3 in the homework posting template. Furthermore, this is not calculus and should be in the precalculus forum.
 

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