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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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