Home
Class 12
MATHS
Which of the following sets of points fo...

Which of the following sets of points form an equilateral triangle? `(a)(1,0),(4,0),(7,-1)` `(b)(0,0),(3/2,4/3),(4/3,3/2)` `(c)(2/3,),(0,2/3),(1,1)` (d) None of these

A

`(1,0),(4,0),(7,-1)`

B

`(0,0),(3//2,4//3),4//3,3//2)`

C

`(2//3,0),(0,2//3),(1,1)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
For the equilateral triangle,one vertex must be an irrational point.
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE ENGLISH|Exercise Multiple correct|13 Videos

  • COORDINATE SYSYEM

    CENGAGE ENGLISH|Exercise Linked|10 Videos

  • COORDINATE SYSYEM

    CENGAGE ENGLISH|Exercise Concept applications 1.6|9 Videos

  • COORDINATE SYSTEM

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

By plotting the following points check whether they are collinear or not (i) (1,1), (2,2),(4,4) (ii) (1,0), (-3,0), (0,0) (iii) (2,-2), (0,0), (-3,4)

Which of the following sets of quantum numbers represent an impossible arrangement :- {:(,n,l,m,m_(s),),((A),3,2,-2,(1)/(2),),((B),4,0,0,(1)/(2),),((C),3,2,-3,(1)/(2),),((D),5,3,0,(1)/(2),):}

which of the following points is on the line of intersection of planes x=3z-4,y=2z-3 ? (A) (4,3,0) (B) (-3,-4,0) (C) (3,2,1) (D) (-4,-3,0)

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0) (ii) (–3, 5), (3, 1), (0, 3), (–1, – 4) (iii) (4, 5), (7, 6), (4, 3), (1, 2)

Which of the following is a non singular matrix? (A) [(1,a,b+c),(1,b,c+a),(1,c,a+b)] (B) [(1,omega, omega^2),(omega, omega^2,1),(omega^2,1,omega)] where omega is non real and omega^3=1 (C) [(1^2,2^2,3^2),(2^2,3^2,4^2),(3^2,4^2,5^2)] (D) [(0,2,-3),(-2,0,5),(3,-5,0)]

Find the centroid of the triangle mid points of whose sides are (1,2,-3),(3,0,1)and (-1,1,4)

Taking 0.5 cm as 1 unit, plot the following points on the graph paper A(1,3), B(-3,-1),C(1,-4),D(-2,3). E(0,-8) and F(1,0).

The orthocentre of the triangle formed by the lines x y=0 and x+y=1 is (a) (1/2,1/2) (b) (1/3,1/3) (c) (0,0) (d) (1/4,1/4)

In A B C , if the orthocentre is (1,2) and the circumcenter is (0, 0), then centroid of A B C) is (a) (1/2,2/3) (b) (1/3,2/3) (c) (2/3,1) (d) none of these

Wherever possible write each of the following as a single matrix. (i) [{:(,1,2),(,3,4):}]+[{:(,-1,-2),(,1,-7):}] (ii) [{:(,2,3,4),(,5,6,7):}]-[{:(,0,2,3),(,6,-1,0):}] (iii) [{:(,0,1,2),(,4,6,7):}]+[{:(,3,4),(,6,8):}]

CENGAGE ENGLISH-COORDINATE SYSYEM -Exercises
  1. A B C is an isosceles triangle. If the coordinates of the base are B(1...

    Text Solution

    |

  2. If two vertices of a triangle are (1,3) and (4,-1) and the area of tri...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. If |x1y1 1x2y2 1x3y3 1|=|a1b1 1a2b2 1a3b3 1| then the two triangles ...

    Text Solution

    |

  6. O P Q R is a square and M ,N are the middle points of the sides P Qa n...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. The polar coordinates equivalent to (-3,sqrt3) are

    Text Solution

    |

  10. If the point x1+t(x2-x1),y1+t(y2-y1) divides the join of (x1,y1) and (...

    Text Solution

    |

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

    Text Solution

    |

  12. In triangle ABC, angle B is right angled, AC=2 and A(2,2), B(1,3) then...

    Text Solution

    |

  13. One vertex of an equilateral triangle is (2,2) and its centroid is (-2...

    Text Solution

    |

  14. ABCD is a rectangle with A(-1,2),B(3,7) and AB:BC=4:3. If P is the cen...

    Text Solution

    |

  15. If (2,-3), (6,-5) and (-2,1) are three consecutive verticies of a rohm...

    Text Solution

    |

  16. If poitns A(3,5) and B are equidistant from H(sqrt2,sqrt5) and B has r...

    Text Solution

    |

  17. Le n be the number of points having rational coordinates equidistant ...

    Text Solution

    |

  18. In a triangle ABC the sides BC=5, CA=4 and AB=3. If A(0,0) and the int...

    Text Solution

    |

  19. If A(0, 0), B(1, 0) and C(1/2,sqrt(3)/2) then the centre of the circle...

    Text Solution

    |

  20. Statement 1: If in a triangle, orthocentre, circumcentre and centroid ...

    Text Solution

    |