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Question
Show that the following points taken in order to form an equilateral triangle
`"A"(2, 2), "B"(-2, -2), "C"(-2sqrt(3), 2sqrt(3))`
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Solution
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((-2 - 2)^2 + (-2 - 2)^2`
= `sqrt((-4)^2 + (-4)^2`
= `sqrt(16 + 16)`
= `sqrt(32)`
BC = `sqrt((-2sqrt(3) + 2)^2 + (2sqrt(3) + 2)^2`
= `sqrt(12 + 4 - 8sqrt(3) + 12 + 4 + 8sqrt(3))`
= `sqrt(16 + 16)`
= `sqrt(32)`
AC = `sqrt((-2sqrt(3) - 2)^2 + (2sqrt(3) - 2)^2`
= `sqrt((2sqrt(3) + 2)^2 + (2sqrt(3) - 2)^2`
= `sqrt(12 + 4 + 8sqrt(3) + 12 + 4 - 8sqrt(3))`
= `sqrt(16 + 16)`
= `sqrt(32)`
AB = BC = AC ...(Three sides are equal)
∴ ABC is an equilateral triangle.
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