Home
Class 9
MATHS
Show that points (2-sqrt3 , sqrt3 +1) , ...

Show that points `(2-sqrt3 , sqrt3 +1) , (1,0)` and `(3,2)` form an equilateral triangle .

Text Solution

Verified by Experts

Let A`(2-sqrt3 , sqrt3 + 1)` , B (1, 0) and C(3,2) be the given points .
`AB = sqrt((1-2 + sqrt3)^(2) + (0-(sqrt3 +1))^(2))`
`= sqrt((sqrt3-1)^(2) + (-1 - sqrt3)^(2))`
AB = `sqrt8` units .
`BC = sqrt((3-1)^(2) + (2-sqrt3)^(2)) = sqrt8` units .
AC = `sqrt((3-(2-sqrt3))^(2) + (2-(sqrt3 +1)^(2)))`
`= sqrt((1+sqrt3)^(2) + (1-sqrt3)^(2)) = sqrt8` units.
`therefore` AB = BC = AC = `sqrt8` units .
Hence , the given points form an equilateral triangle .
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    PEARSON IIT JEE FOUNDATION|Exercise Very short Answer Question|30 Videos

  • COORDINATE GEOMETRY

    PEARSON IIT JEE FOUNDATION|Exercise Short Answer Type Questions|15 Videos

  • BANKING AND COMPUTING

    PEARSON IIT JEE FOUNDATION|Exercise Level 3|6 Videos

  • GEOMETRY

    PEARSON IIT JEE FOUNDATION|Exercise CONCEPT APPLICATION|61 Videos

Similar Questions

Explore conceptually related problems

For what value of alpha ,the points (1,2,3),(2,3,1) and (3,1,alpha) form an equilateral triangle?

If three points (0,0),(3,sqrt(3)) and (3,lambda) form an equilateral triangle,then lambda=(a)2 (b) -3(c)-4(d) None of these

Knowledge Check

  • Evaluate lamda , if three points (0, 0), (3, sqrt3) and (3, lamda) form an equilateral triangle.

    A
    `-4`
    B
    2
    C
    `-3`
    D
    `pmsqrt3`

  • If the points (1, 1), (-1, -1) and (-sqrt(3),k) are vertices of a equilateral triangle then the value of k will be : (a)1 (b)-1 (c) sqrt3 (d) -sqrt3

    A
    1
    B
    -1
    C
    `sqrt3`
    D
    `-sqrt3`

    • Similar Questions

    Explore conceptually related problems

    Prove that the triangle formed by joining the three points whose coordinates ere (1,2,3),(2,3,1) and (3,1,2) is an equilateral triangle.

    Show that the points (1,-2,-3),(2,-3,-1) and (3,-1,-2) are the vertices of an equilateral triangle

    Show that the points (a,a),(-a,-a)and(-sqrt3a,sqrt3a) are the vertices of an equilateral triangle. Find its area.

    If the points (1,1),(-1,-1) and (-sqrt(3),k) are vertices of a equilateral triangle then find thevalues of k .

    Show that the points A(1,2),B(1,6), C(1 + 2sqrt(3),4) are the vertices of an equilateral triangle .

    Using distance formula,prove that the points (-1+sqrt(3)i)/(2) and (-1-sqrt(3)i)/(2) form the vertices of an equilateral triangle in complex plane.

    Home
    Profile