Question

show that the points (2,4),(2,6) (2+root3,5) form an equilateral triangle

Answer 1

Hiii friend,

Let the given points be A(2,4) , B(2,6) and C(2+✓3,5).

Using distance formula we have.

A(2,4) and B(2,6)

Here,

X1 = 2 , Y 1 = 4 , X2 = 2 and Y2 = 6

Therefore,

AB² = (X2-X1)² + (Y2-Y1)²

AB² = (2-2)² + (6-4)² => 0+4= 4.

B(2,6) and C(2+✓3,5)

Here,

X1= 2 , Y1 = 6 and X2 = 2+✓3 , Y2 = 5

Therefore,

BC² = (X2-X1)² + (Y2-Y1)²

BC² = (2+✓3-2)² + (5-6)² = (✓3)² + (-1)² = 3+1 = 4.


A(2,4) and C(2+✓3,5)

Here,

X1 = 2 , Y1 = 4 and X2 = 2+✓3 , Y2 = 5

Therefore,

AC²= (X2-X1)² + (Y2-Y1)²

AC² = (2+✓3-2)² + (5-4)² = (✓3)² + (1)² = 3+1 = 4

AB = BC = AC = 4

Hence,

∆ABC is a equilateral triangle and each it's sides is 4 .

HOPE IT WILL HELP YOU...... :-)

Answer 2

Sorry for hand writting


I hope this will help you


-by ABHAY