Equidistant? Type it as written
Skip the distance formula: type distance() = distance() and Desmos finds the point.
1:41 · Coordinate Geometry
Worked in this video
In the xy-plane, point P lies on the line y = 2x − 1 and is the same distance from (1, 1) as it is from (5, 3).
What is the x-coordinate of P?
On paper this is the distance formula twice, both sides squared and set equal, and a page of algebra. In Desmos, use the fact that P is on the line, so P = (x, 2x − 1). Type distance((x, 2x − 1), (1, 1)) = distance((x, 2x − 1), (5, 3)). That is an equation in x alone, so Desmos draws it as a vertical line at x = 2.25, and P = (2.25, 3.5).
Answer: x = 2.25