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Question
Show that the following points taken in order to form an equilateral triangle
`"A"(sqrt(3), 2), "B"(0, 1), "C"(0, 3)`
Solution
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((0 - sqrt(3))^2 + (1 - 2)^2`
= `sqrt((- sqrt(3))^2 + (-1)^2`
= `sqrt(3 + 1)`
= `sqrt(4)`
= 2
BC = `sqrt((0 - 0)^2 + (3 - 1)^2`
= `sqrt(0^2 + 2^2)`
= `sqrt(4)`
= 2
AC = `sqrt((0 - sqrt(3))^2 + (3 - 2)^2`
= `sqrt((- sqrt(3))^2 + 1^2)`
= `sqrt(3 + 1)`
= `sqrt(4)`
= 2
AB = BC = AC ...(Three sides are equal)
∴ ABC is an equilateral triangle.
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