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Show that the points (a , a),(-a ,-a) an...

Show that the points `(a , a),(-a ,-a)` and `(-sqrt(3)a ,sqrt(3)a)` are the vertices of an equilateral triangle. Also, find its area.

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Let the points be represented by `A(a,a),B(-a,-a)` and `C(-asqrt3,sqrt3)`Using the distance formula
`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)` we have
`AB=sqrt((a+a)^2+(a+a)^2)`
`sqrt((2a)^2+(2a)^2)=sqrt(4a^2+4a^2)=sqrt(8a^2)=2sqrt2a`
...
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