Question

if the points (1,1) ,(-1,-1), and (-√3,k) are the vertices of an equilateral triangle then k=?


The answer seems to be √3
how?

plz help me with correct and complete solution​

Answer 1

Answer:

√3

Step-by-step explanation:

In equilateral triangle, length of sides is equal.

So,

Length of (1,1) and (-1,-1) is equal to the length of (-1,-1) and (-√3,k).

Using formula,

= > √{(- 1 - 1)² + (- 1 - 1 )²} = √{(- √3 -(-1))² + (k -(-1))² }

= > (-2)² + (-2)² = (- √3 + 1)² + ( k + 1 )²

= > 4 + 4 = (√3)² + (1)² - 2√3 + (k + 1)²

= > 8 = 3 + 1 - 2√3 + (k + 1)²

= > 8 - 4 + 2√3 = (k + 1)²

= > 4 + 2√3 = (k + 1)²

= > 3 + 1 + 2√3 = (k + 1)²

= > (√3)² + (1)² + 2√3 = (k + 1)²

= > (√3 + 1)² = (k + 1)²

= > √3 + 1 = k + 1

= > √3 = k