Question

prove that points (2a,4a), (2a,6a), and (2a +√3a,5a) are the vertices of an equilateral triangle of side

Answer 1

Let A (2a, 4a)

B(2a, 6a)

C (2a + sqrt (3a), 5a)

Side AC:

`\sqrt{(2a+√(3a)-2a)^2+(5a-4a)^2 }=√(3a+a^2)`

Side BC:

`\sqrt{(2a+√(3a)-2a)^2+(5a-6a)^2 }=√(3a+a^2)`

Hence AC = BC

It is an isoceles triangle.

Side AB:

`√((2a-2a)^2+(6a-4a)^2 )=√(2a^2)=2a`

It proves that the triangle is NOT an equilateral triangle.