Home
Class 12
MATHS
Let P be (5, 3) and a point R on y=x and...

Let `P` be (5, 3) and a point `R` on `y=x` and `Q` on the x-axis be such that `P Q+Q R+R P` is minimum. Then the coordinates of `Q` are `((17)/4,0)` (b) `(17 ,0)` `((17)/2,0)` (d) none of these

A

(17/4,0)

B

(17,0)

C

(17/2,0)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A

P' and P'' are the images of P w.r.t. y=x and y=0, respectively.
Therefore, `P'-=(3,5).`
The equation of P'P'' is
`y+3 = (5+3)/(3-5)(x-5)`

`therefore x=5+3(-(1)/(4)) = (17)/(4)`
`therefore Q-=((17)/(4),0)`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise (Multiple)|30 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise (Comprehension)|27 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise 2.6|5 Videos

  • STRAIGHT LINE

    CENGAGE|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|9 Videos

Similar Questions

Explore conceptually related problems

Let P be (5,3) and a point R on y = x and Q on the X - axis be such that PQ +QR+RP is minimum ,then the coordinates of Q are

A light ray emerging from the point source placed at P(2,3) is reflected at a point Q on the y-axis. It then passes through the point R(5,10)dot The coordinates of Q are (0,3) (b) (0,2) (0,5) (d) none of these

Let O(0,0),P(3,4), and Q(6,0) be the vertices of triangle O P Q . The point R inside the triangle O P Q is such that the triangles O P R ,P Q R ,O Q R are of equal area. The coordinates of R are (a) (4/3,3) (b) (3,2/3) (c) (3,4/3) (d) (4/3,2/3)

A man starts from the point P(-3,4) and reaches the point Q(0,1) touching the x-axis at R(alpha,0) such that P R+R Q is minimum. Then 5|alpha| (A) 3 (B) 5 (C) 4 (D) 2

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

If sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-2) (b) p^2=q(q+2) (c) p^2q^2=2q (d) none of these

The image of P(a ,b) on the line y=-x is Q and the image of Q on the line y=x is R . Then the midpoint of P R is (a) (a+b ,b+a) (b) ((a+b)/2,(b+2)/2) (c) (a-b ,b-a) (d) (0,0)

A point R with x-coordinate 4 lies on the line segment joining the points P(2,-3,4) and Q(8,0,10) . Find the coordinates of the point R.

The vertices of a triangle are (p q ,1/(p q)),(q r ,1/(q r)), and (r q ,1/(r p)), where p ,q and r are the roots of the equation y^3-3y^2+6y+1=0 . The coordinates of its centroid are (1,2) (b) 2,-1) (1,-1) (d) 2,3)

CENGAGE-STRAIGHT LINES-Exercise (Single)
  1. Two A(0,0) and B(x , y) with x in (0,1) and y > 0. Let the slope of li...

    Text Solution

    |

  2. A triangle is formed by the lines x+y=0,x-y=0, and l x+m y=1. If la n ...

    Text Solution

    |

  3. Let P be (5, 3) and a point R on y=x and Q on the x-axis be such that ...

    Text Solution

    |

  4. If a pair of perpendicular straight lines drawn through the origin ...

    Text Solution

    |

  5. A point P(x,y) moves that the sum of its distance from the lines 2x-y-...

    Text Solution

    |

  6. If AD, BE and CF are the altitudes of Delta ABC whose vertex A is (-4,...

    Text Solution

    |

  7. The vertex A of DeltaABC is (3,-1). The equation of median BE and angl...

    Text Solution

    |

  8. Suppose A, B are two points on 2x-y+3=0 and P(1,2) is such that PA=PB....

    Text Solution

    |

  9. about to only mathematics

    Text Solution

    |

  10. A light ray coming along the line 3x+4y=5 gets reflected from the line...

    Text Solution

    |

  11. The point A(2,1) is translated parallel to the line x-y=3 by a distanc...

    Text Solution

    |

  12. One of the diagonals of a square is the portion of the line x/2+y/3=2 ...

    Text Solution

    |

  13. The point P(2,1) is shifted through a distance 3sqrt(2) units measured...

    Text Solution

    |

  14. Let O be the origin. If A(1,0)a n dB(0,1)a n dP(x , y) are points such...

    Text Solution

    |

  15. In a triangle A B C , the bisectors of angles Ba n dC lies along the l...

    Text Solution

    |

  16. Line a x+b y+p=0 makes angle pi/4 with xcosalpha+ysinalpha=p ,p in R^...

    Text Solution

    |

  17. The equation of the line AB is y = x. If A and B lie on the same side ...

    Text Solution

    |

  18. The equation of the bisector of the acute angle between the lines 2x-y...

    Text Solution

    |

  19. The straight lines 4a x+3b y+c=0 , where a+b+c (4,3) (b) (1/4,1/3...

    Text Solution

    |

  20. If the lines a x+y+1=0,x+b y+1=0a n dx+y+c=0(a ,b ,c being distinct...

    Text Solution

    |