If an equilateral triangle ABC is drawn as shown below with A(0,0) and a side of 4 units then the other two vertices of the triangle are___
C=(2,2√3)
B =(4,0)
In equilateral triangle ABC draw CD⊥ to AB, then D will be the mid-point of AB.
∵B is on X-axis and AB =4 ∴B=(4,0)
∵ Given AB =4
⇒AD=12×AB
=2 units.
∴x coordinate of C is 4.
Now ADC makes right angled triangle with ∠ADC=90∘
∴AC2=AD2+DC2
⇒42=22+DC2
⇒DC2=16−4
=12
⇒DC=2√3
∴ Coordinates of C=(2,2√3)
∴ Remaining vertices are B(4,0) and C=(2,2√3)