Home
Class 11
MATHS
The point (4,1) undergoes the following ...

The point (4,1) undergoes the following transformation successively
(i) Reflection about the line y=x
(ii) Translation through a distance 2 unit along the positive direction (x-axis)
(iii)Rotation through on angle `pi//4` about origin in anticlockwise direction.
Then the co-ordinates of the final points

A

`(1/sqrt2,7/sqrt2)`

B

`(-1)/sqrt2,7/sqrt2)`

C

`(-1)/sqrt2,(-7)/sqrt2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

Similar Questions

Explore conceptually related problems

The point (4,1) undergoes the following three transformations successively (a) Reflection about the line y=x (b)Translation through a distance 2 units along the positive direction of the x-axis ( c) Rotation through an angle pi//4 about the origin in the anti clockwise direction. The final position of the point is given by the co-ordinates

Point P(2,3) goes through following transformations in successtion: (i) reflection in line y=x (ii) translation of 4 units to the right (iii) translation of 5 units up (iv) reflection in y-axis Find the coordinates of final position of the point .

The distance of a point from the x-axis in the positive direction is 5 and from the y-axis in the positive direction is 7. Find the co-ordinates of the point.

(xvi) The distance of a point from the x-axis is 7 units on the negative directions and the distance from the y-axis is 8 units on the positive direction. Find the co-ordinates or the point.

The point represented by the complex number (2-i) is rotated about origin through an angle of pi/2 in clockwise direction. The new position of the point will be-

A line makes an acute angle with the positive direction of x-axis and passes through the points (6, -7, -1) and (2, -3, 1), find the direction cosines of the line.

Angle of a line with the positive direction of the x-axis is theta . The line is rotated about some point on it in anticlockwise direction by angle 45^0 and its slope becomes 3. Find the angle theta

The point represented by the complex number 2-i is rotated about origin through an angle pi/2 in the clockwise direction. the complex number corresponding to new position of the point is

Determine x so that the line passing through (3,4) and (x ,5) makes an angle of 135^0 with the positive direction of the x-axis.

Find the distance from the point P(4,1) to the line 4x-y=0 measured along the line making and angle 135^(@) with the positive direction of x-axis.

PATHFINDER-CARTESIAN COORDINATES AND STRAIGHT LINE-QUESTION BANK
  1. If the angle between the two lines represented by 2x^2 + 5xy + 3y^2 + ...

    Text Solution

    |

  2. The equation of second degree x^2 + 2sqrt2 xy + 2y^2 + 4x + 4 sqrt2 y ...

    Text Solution

    |

  3. The point (4,1) undergoes the following transformation successively (i...

    Text Solution

    |

  4. Mixed term xy is to be removed from the general equation of second deg...

    Text Solution

    |

  5. For points P=(x1,y1)and Q =(x2,y2) of the co-ordinate plane a new dist...

    Text Solution

    |

  6. The orthocentre of the triangle formed by the lines x+y=1,2x+3y=6and 4...

    Text Solution

    |

  7. A straight line L with negative slope passes through the point (8,2) a...

    Text Solution

    |

  8. The distance between the circumcentre and orthocentre of the triangle ...

    Text Solution

    |

  9. If P(1+alpha/sqrt2 ,2+ alpha/sqrt2) be any point on a line, then the r...

    Text Solution

    |

  10. If the point (a,a) fall between the lines |x+y|=2,then

    Text Solution

    |

  11. Two fixed point A and B are taken on the cordinate axes such that OA =...

    Text Solution

    |

  12. A variable line through the point of intersection of the lines x/a+y/b...

    Text Solution

    |

  13. The equations of the line passing through the point of intersection o...

    Text Solution

    |

  14. A ray of light travelling along the line 2x-3y+5=0 ,after striking a p...

    Text Solution

    |

  15. Line L has intercepts a and b on the coordinate axes. When the axes ar...

    Text Solution

    |

  16. Consider the point A(3,4) and B(7,13).If P be a point on the line y=x,...

    Text Solution

    |

  17. Consider the point A(3,4) and B(7,13).If P be a point on the line y=x,...

    Text Solution

    |

  18. The number of integral values of 'm' for which the x coordinate of the...

    Text Solution

    |

  19. The diagonals of the parallelogram whose sides are lx+my+n=0,lx+my+n'=...

    Text Solution

    |

  20. Let PQR be a right angled isosceles triangle, right angled at P(2,1). ...

    Text Solution

    |