Question

Find the co-ordinates of the point, where the origin is shifted, axes remaining parallel, if the old and new co-ordinates of the points are given, in each of the following.

Old co-ordinates i) (2, 3) ii) (3, -4) iii) (a, b)

New co-ordinates (5, -2} (7, 2) (c, d)

Answer 1

Old coordinates $(x,y)=(2,3)$

new coordinates $(x,y)=(5,-2)$

if origin is shifted from $(0,0)$ is $(\alpha ,\beta )$

new coordinates $=(x,y)=(x-\alpha ,y-\beta )$

$\Rightarrow (5,-2)=(2-\alpha ,3-\beta )$

$\Rightarrow \alpha =2-5;\beta =3+2$

$\Rightarrow (\alpha ,\beta )=(-3,5)$

$\therefore originisshiftedto(-3,-5)$

$\left(ii\right)$

old coordinates $(x,y)=(3,-4)$

new coordinates $(x,y)=(7,2)=(x-\alpha ,y-\beta )$

$(7,2)=(3-\alpha ,4-\beta )$

$\alpha =3-7;\beta =-4-2$

$\therefore (\alpha ,\beta )=(-4,-6)$

$\therefore originisshiftedto(-4,-6)$

$\left(iii\right)$

old coordinates $(x,y)=(a,b)$

new coordinates $(x,y)=(c,d)$

$(c,d)=(a-\alpha ,b-\beta )$

$\Rightarrow \alpha =a-c;\beta =b-d$

$\Rightarrow (\alpha ,\beta )=(a-c,b-d)$

$\therefore originisshiftedto(a-c,b-d)$