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

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

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

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

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-

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 .

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.

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

Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30^(@) with positive direction of the x-axis.

A line which makes an acute angle theta with the positive direction of the x-axis is drawn through the point P(3,4) to meet the line x=6 at R and y=8 at Sdot Then,

The line joining the points (x ,2x)a n d(3,5) makes an obtuse angle with the positive direction of the x-axis. Then find the values of xdot

If the pair of lines sqrt(3)x^2-4x y+sqrt(3)y^2=0 is rotated about the origin by pi/6 in the anticlockwise sense, then find the equation of the pair in the new position.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. If two vertices of a triangle are (-2,3) and (5,-1) the orthocentre li...

    Text Solution

    |

  2. P and Q are points on the line joining A(-2,5) and B(3,1) such that AP...

    Text Solution

    |

  3. The point (4,1) undergoes the following three transformations successi...

    Text Solution

    |

  4. If the coordinates of the vertices of a triangle are rational numbers,...

    Text Solution

    |

  5. If P(1,2) ,Q(4,6),R(5,7), and S(a , b) are the vertices of a parallelo...

    Text Solution

    |

  6. If the area of the triangle formed by the points (2a ,b)(a+b ,2b+a), a...

    Text Solution

    |

  7. The incenter of the triangle with vertices (1,sqrt(3)),(0,0), and (2,...

    Text Solution

    |

  8. The locus of the moving point whose coordinates are given by (e^t+e^(-...

    Text Solution

    |

  9. The distance between the circumcenter and the orthocenter of the trian...

    Text Solution

    |

  10. A man starts from the point P(-3, 4) and reaches point Q (0,1) touchin...

    Text Solution

    |

  11. Statement 1 : The area of the triangle formed by the points A(1000 ,...

    Text Solution

    |

  12. Consider three points P-=(-sin(beta-alpha),-cosbeta), Q-=(cos(beta-alp...

    Text Solution

    |

  13. Factorise: (l+m)^2–4lm

    Text Solution

    |

  14. Find |vecx| if for a unit vector, veca , (vecx-veca).(vecx+veca)=12,

    Text Solution

    |

  15. A straight line passing through P(3,1) meets the coordinate axes at A ...

    Text Solution

    |

  16. Let A-=(3,-4),B-=(1,2). Let P-=(2k-1,2k+1) be a variable point such th...

    Text Solution

    |

  17. If |{:(x1,,y1,,1),(x2,,y2,,1),(x3,,y3,,1):}|=|{:(a1,,b1,,1),(a2,,b2,,1...

    Text Solution

    |

  18. OPQR is a square and M,N are the middle points of the sides of PQ nad ...

    Text Solution

    |

  19. Which of the following sets of points form an equilateral triangle? (...

    Text Solution

    |

  20. A particle p moves from the point A(0,4) to the point 10 ,-4) . The pa...

    Text Solution

    |