1.

Show that the points (1,1),(-1,-1) and (-sqrt3,sqrt3) are the vertices of an equilateral triangle.

Answer»

Solution :
`THEREFORE absbar(AB) = sqrt((-1-1)^2 + (-1-1)^2) = 2sqrt2` Slope of
`absbar(BC) sqrt((-1+sqrt3)^2 + (-1-sqrt3)^2)`
= `sqrt(2)(1+3) = 2sqrt2`
`absbar(AC) = sqrt((1+sqrt3)^2 + (1-sqrt3)^2)`
= sqrt(2)(1+3) = 2sqrt2`
`therefore BARAB = barBC = barAC`
`therefore` ABC is an equilateral TRIANGLE.


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