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The origin is translated to (1,2) . The ...

The origin is translated to (1,2) . The point (7,5) in the old system undergoes the following transformations successively.
(i) Moves to the new point under the given translation of origin
(ii) Translated through 2 units along the negative direction of the new X-axis
(iii) Rotated through an angle `(pi)/(4)` about the origin of new system in the clockwise direction
The final position of the point (7,5) is

A

`(9/sqrt(2),-1/sqrt(2))`

B

`(7/sqrt(2), 1/sqrt(2))`

C

`(7/sqrt(2), -1/sqrt(2))`

D

`(5/sqrt(2), -1/sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-TRANSFORMATION OF AXES -EXCERSIE 1
  1. The transformed equation of x^(2) - 2sqrt(3)xy -y^(2) =2a^(2) when the...

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  2. When the axes are rotated through an angle pi//6. Find the transformed...

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  3. The transformed equation of x^(2) - 2sqrt(3)xy -y^(2) =2a^(2) when the...

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  4. The transformed equation of 3x^(2) + 3y^(2) + 2xy =2 when the coordina...

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  5. The transferred equation of x^(2) -y^(2) +a^(2)=0 when the axes are ro...

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  6. The transformed equation of x^(2) + y^(2) =a^(2) when the axes are rot...

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  7. The transformed equation of x^(2) + y^(2) =r^(2) when the axes are rot...

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  8. The transformed equation of x^(2)//a^(2) -y^(2)//b^(2)=1 when the axes...

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  9. The transformed equation of ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c=0 w...

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  10. The transformed equation of x^(2) + y^(2) - 4x + 6y-12=0 when the axes...

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  11. If the axes are rotated through, an angle theta, the transformed equat...

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  12. If the transformed equation of a curve is 17x^(2) - 16xy + 17y^(2)=225...

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  13. If the transferred equation of a curve is x^(2) + 2sqrt(3)xy - y^(2) =...

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  14. The angle of rotation of the axes so that the equation sqrt(3)x - y+5=...

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  15. The angle of rotation of the axes so that the equation sqrt(3)x - y+5=...

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  16. The angle of rotation of the axes so that the equation x + y-6=0 may b...

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  17. The line joining two points A(2,0), B(3,1) is rotated about A in antic...

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  18. The point (4,1) undergoes the following transformations successively ...

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  19. The point P(1,3) undergoes the following transformations successively ...

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  20. The origin is translated to (1,2) . The point (7,5) in the old system ...

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