“What seems to us as bitter trials are often blessings in disguise.” –Oscar Wilde

# Lecture - 19 Chapter 10 Straight Lines

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)

**(**(o, 1)

*ii*)**(**(5, 0)

*iii*)**(**(-1, -2)

*iv*)**(**(3, -5)

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

**(**\( xy-y^2-x+y=0\)

*ii*)**(**\( xy-x-y+1=0\)

*iii*)