Analytic Geometry

[davekristian]

Find the equation of locus of the
3rd vertex of isosceles triangle. If one of its equal sides joins the points (1,5) and (4,0)..

My exam is approaching..
But i always got stock in this problem..
Pls help me to understand..

 

[HallsofIvy]

That's pretty straight forward isn't it? We are given that the segment between (1, 5) and (4, 0) is one of the equal sides. The length of that side is \(\displaystyle \sqrt{(4- 1)^2+ (5- 0)^2}=\sqrt{34}\). The other equal side must emanate from either (1, 5) or (4, 0). What is the equation of all points at distance \(\displaystyle \sqrt{34}\) from (1, 5) (what geometric shape is that?). What is the equation of all points at distance \(\displaystyle \sqrt{34}\) from (4, 0)?