How do I find the equidistant point?

1. Aug 29, 2007

BankaiNinja

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

2. Aug 29, 2007

BankaiNinja

does anyone know?

3. Aug 29, 2007

BankaiNinja

nobody?

4. Aug 29, 2007

turdferguson

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)

5. Aug 29, 2007

BankaiNinja

huh? can u show me? step by step

6. Aug 29, 2007

nicktacik

The distance between a point (x,y) and the point (-3,4) is $$d1=\sqrt{(x+3)^2 + (y-4)^2}$$. The distance between a point (x,y) and the point (0,0) is $$d2 = \sqrt{x^2 + y^2}$$. You know what y is from the equation of the line, so substitute that, set d1=d2, and solve for x.

7. Aug 29, 2007

cristo

Staff Emeritus
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.