Finding The Equidistant of 2 Points

[Ecom]

Homework Statement

I need the formula for finding the coordinates of the point on the y-axis that are equildistant from two other pair of points (3,0) and
(3,6).

Homework Equations

i don't know, but these might have something to do with it.

[tex]\sqrt{}[/tex] (y₂-y₁)²+(x₂-x₁)²

(x₂+x₁[tex]/[/tex]2, y₂+y₁[tex]/2[/tex])

The Attempt at a Solution

I found the midpoint of (3,0)-(3,6), and found the distance between the midpoint to the endpoints, but i don't know were to got from there. I also tried writing random scribbles on my graph papers, crying, begging God to take me out of IB extended math, and finally, posting on Physics Forums for help.

 

[LCKurtz]

Hint: Points equidistant from your two points would be on the perpendicular bisector of the line joining them. Draw a sketch.

 

[Ecom]

Hint: Points equidistant from your two points would be on the perpendicular bisector of the line joining them. Draw a sketch.

Ah Yes, but that would be too easy! I need to find the anwser using an equation.

 

[LCKurtz]

Sure. Solve for the mid-point between your points. Write the equation of the perpendicular bisector. Solve for where it hits the y axis. The picture was just to lead the way.

 

[Ecom]

ohhhhhhhhhhh...

Probably should have looked up "perpendicular bisector". I knew what perpendicular meant, but you threw me off at bisector.

Anyway, thanks for the information. Saved me hours of going over "attempt at solution" again

 

[HallsofIvy]

This is particularly simple because it is a vertical line. Any line perpendicular to it is a horizontal line and has the equation "y= constant". But the problem is finding that constant. To do that you need to know the y-component of the midpoint, which was what the original question asked!

It should be obvious what the x-component is. What point is half way between 0 and 6 on the number line?