The starting point of a line that is not at the origin is simply called a point (often just “the initial point” or “starting point” of the line). In most school and college math contexts, the word “origin” is reserved for the special point (0,0)(0,0)(0,0) on a coordinate plane, but any line can begin at any other point such as (3,5)(3,5)(3,5) or a labeled point AAA. A line segment or ray that begins at a point other than the origin is still described using that point as its starting position, for example “the directed line segment from PPP to QQQ” where PPP is the starting point.

Quick Scoop

In geometry, we don’t use a special, different name for “the starting point of a line that is not at the origin” — we just treat it as a regular point and, when direction matters, call it the starting or initial point.

This is a bit like saying: the race doesn’t have to start at home base; the place you choose to start becomes your reference point.

What do we call that starting point?

  • It is called a point in geometry.
  • When direction matters (like with a ray or a directed line segment), it is often called the starting point , initial point , or tail of the segment/vector.
  • Only the point (0,0)(0,0)(0,0) on a coordinate grid is the origin ; everything else is just another point.

So if you have a line segment from PPP to QQQ:

  • PPP is the starting point (initial point).
  • QQQ is the endpoint (or tip).

Mini sections

Lines vs segments vs rays

  • A line extends forever in both directions, so we usually describe it by “passing through points AAA and BBB” rather than having a unique start or end.
  • A line segment has two endpoints; you can pick one as the “starting point” depending on the context.
  • A ray has one fixed starting point and extends forever in one direction; that fixed point is its starting or initial point.

In more advanced language, a “directed line segment from PPP to QQQ” is literally defined as an arrow with starting point PPP and tip QQQ.

Coordinate systems and “not at the origin”

On a coordinate plane:

  • The origin is strictly the point (0,0)(0,0)(0,0).
  • Any other point, like (2,−1)(2,-1)(2,−1) or labeled point AAA, can serve as the starting point of your line segment or ray.
  • You might hear phrases like “a line that does not go through the origin,” but its starting point is still just “point PPP” or “point AAA.”

Example:
If you draw a ray starting at (3,4)(3,4)(3,4) and going upwards, you would call it “a ray with starting point (3,4)(3,4)(3,4)” — not “an origin,” because (3,4)(3,4)(3,4) is not (0,0)(0,0)(0,0).

Numbered recap

  1. In geometry, we reserve the word origin for (0,0)(0,0)(0,0) on a coordinate plane.
  1. A line, segment, or ray can start at any point, such as PPP or (3,5)(3,5)(3,5).
  2. That starting location is called a point , more specifically the starting or initial point when direction matters.
  1. There is no special, different name used only for “starting point not at the origin” — the same terminology applies everywhere.

TL;DR

The starting point of a line that is not at the origin is just a point, usually referred to as the starting point or initial point of the line, segment, ray, or directed line segment.

Information gathered from public forums or data available on the internet and portrayed here.