What are loci? What is loci and symmetry? How do you use them? Do they have any specific formulae to work with? What are they used for? Please help!
Locus is path described by the point under given condition. Loci is plural form of the word locus.
For example for defining circle, we say a point is moving in such a way that always remains equidistance from a fixed point. Here fixed point is known as center and the path described by the point is circumference of the circle.
Let P(x,y) is moving point. C(x1,y1) is fixed point .
This is locus of moving point P.
Symmetry you can say image (congruence ) of the object . For example You left palm and right palm are symmetrical.
Symmetry we apply to siplify /visualise the problem and to avoid repitition.
No there are no specific formulas for these. Either for locus or for symmetry conditions prescribed in advance.