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Find the new coordinates of (2,3) if (...

Find the new coordinates of `(2,3)` if
(i) Origin is shifted to `(1,1)`
(ii) Axis are rotated by an angle of `45^(@)` in anticlockwise sence.

Text Solution

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(i) `X=x-h,Y=y-kherex=2,y=3,h=1,k=1`
`impliesX=2-1=1,Y=3-1=2`
Hence `(1,2)`
(ii) `2=Xcos45^(@)-Ysin45^(@)" "...(i)`
`3=Xsin45^(@)+Ycos45^(@)" "...(ii)`
,By (i),(ii) `X-Y=2sqrt2`
`X+Y=3sqrt2`
`X=(5sqrt2)/(2),Y=(sqrt2)/(2)`
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