# Math Help - Rotation in Cartesian Coordinates

1. ## Rotation in Cartesian Coordinates

Hi everyone,

Suppose I have two sets of 4 points in cartesian coordinates:
First set: {a={x1,y1,z1},b={x2,y2,z2},c={x3,y3,z3},d={x4,y4,z 4}}
Secons set: {e={x5,y5,z5},f={x6,y6,z6},g={x7,y7,z7},h={x8,y8,z 9}}

1) How can I check whether the second set can be obtained by translating and rotating the first set?

2) Suppose I know that the second set is the translated and rotated version of the first set. I assume that after transformation "a" becomes "e", "b" becomes "f", "c" becomes "g" and "d" becomes "h". How can I find the translation and rotation matrices T and R such that e=T+R.a, f=T+R.b etc.