15–36 Mathematics Programs
7. Press
X
N to start the old–to–new transformation routine.
8. Key in X and press
g
.
9. Key in Y, press
g
, and see the x–coordinate, U, in the new system.
10. Press
g
and see the y–coordinate, V, in the new system.
11. For another old–to–new transformation, press
g
and go to step 8. For a
new–to–old transformation, continue with step 12.
12. Press
X
O to start the new–to–old transformation routine.
13. Key in U (the x–coordinate in the new system) and press
g
.
14. Key in V (the y–coordinate in the new system) and press
g
to see X.
15. Press
g
to see Y.
16. For another new–to–old transformation, press
g
and go to step 13. For an
old–to–new transformation, go to step 7.
Variables Used:
M
The x–coordinate of the origin of the new system.
N The y–coordinate of the origin of the new system.
T The rotation angle,
θ
, between the old and new systems.
X The x–coordinate of a point in the old system.
Y The y–coordinate of a point in the old system.
U The x–coordinate of a point in the new system.
V The y–coordinate of a point in the new system.
Remark:
For translation only, key in zero for T. For rotation only, key in zero for M and N.
Example:
For the coordinate systems shown below, convert points P
1
, P
2
and P
3
,which are
currently in the (X, Y) system, to points in the (X', Y') system. Convert point P'
4
,
which is in the (
X',Y') system, to the (X,Y) system.
