What is the term for a set of loci that are the same?

  • I
  • Thread starter swampwiz
  • Start date
  • #1
385
18
I'm thinking the term is congruent.

For example, let's say there are 2 parametric lines:

s0( t ) = < 2 , 1 > t + < 0 , - 3 >

s1( t ) = < -18 , -9 > t + < -6 , -6 >

The loci for both are the same line, just that one proceeds in the opposite as the other (and at a high rate) per change in parameter, and such that

s1( - t ) = s0( 9 t + 3 )

Surely, there must be a term for this.
 

Answers and Replies

  • #2
BvU
Science Advisor
Homework Helper
14,269
3,631
'The loci are identical' is the way I would express it.
 
  • #3
34,823
6,567
For example, let's say there are 2 parametric lines
s0( t ) = < 2 , 1 > t + < 0 , - 3 >

s1( t ) = < -18 , -9 > t + < -6 , -6 >
I would say that the equations are equivalent, as both parametric equations describe the same set of points.

For your parametric line, there are an infinite number of parametric representations. For example, the direction along your line is given by the vector <2, 1>. Any scalar multiple of this vector will also have the same direction. In your second equation the direction vector is <-18, -9>, which is -9 * <2, 1>.
Also, the equation could be written using any point on the line.

In slope intercept form, the equation of the line is y = (1/2) x - 3, which could also be written as 2y - x + 6 = 0, and in many other ways as well.
 

Related Threads on What is the term for a set of loci that are the same?

Replies
5
Views
162
Replies
6
Views
2K
Replies
1
Views
1K
Replies
10
Views
19K
  • Last Post
Replies
14
Views
1K
Replies
6
Views
650
Replies
6
Views
2K
Replies
5
Views
9K
Top