# Show that the Points (-3, -3),(3,3) and C (-3 Sqrt(3) , 3 Sqrt(3)) Are the Vertices of an Equilateral Triangle. - Mathematics

Show that the points (-3, -3),(3,3) and C (-3 sqrt(3) , 3 sqrt(3)) are the vertices of an equilateral triangle.

#### Solution

Let the given points be(-3, -3),(3,3) and C (-3 sqrt(3) , 3 sqrt(3)) Now

AB = sqrt((-3-3)^2 +(-3-3)^2) = sqrt((-6)^2 +(-6)^2)

= sqrt(36+36) = sqrt(72) = 6sqrt(2)

BC = sqrt((3+3sqrt(3))^2 +(3-3sqrt(3))^2)

= sqrt(9+27+18sqrt(3) +9+27-18sqrt(3)) = sqrt(72)=6 sqrt(2)

AC = sqrt((-3+3sqrt(3))^2 +(-3-3sqrt(3))^2 )= sqrt((3-3sqrt(3))^2 +(3+3sqrt(3))^2)

= sqrt(9+27-18sqrt(3)+9+27+18sqrt(3)

= sqrt(72)=6sqrt(2)

Hence, the given points are the vertices of an equilateral triangle.

Concept: Area of a Triangle
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 23