Question

Show that the following points taken in order to form an equilateral triangle

`"A"(sqrt(3), 2), "B"(0, 1), "C"(0, 3)`

Answer 1

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.