# Lecture-19

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Purpose of coordinate axes
Geometric Shapes follows “rigid body motion”
All equations have two information related to geometric shapes
Geometrical proof for benefits of shifting of origin
Transformation or translation of axes has two parts : shifting of origin and rotation of axes
Derivation for relation between new origin, old coordinate and new coordinate

 SUPPLEMENTARY EXERCISE 10.5

Question 1. Find the new coordinates of the points in each of the following cases if the origin is shifted to the point (-3, -2) by a translation of axes.
(i) (1, 1)
(ii) (o, 1)
(iii) (5, 0)
(iv) (-1, -2)
(v) (3, -5)

Question 2. Find what the following equations become when the origin is shifted to the point (1, 1)
(i) $x^2+xy-3y^2-y+2=0$
(ii) $xy-y^2-x+y=0$
(iii) $xy-x-y+1=0$