If the three points , , and are vertices of an equilateral triangle, then the values of are
Explanation for the correct option.
Step 1. Understanding the problem.
Let the points be denoted as and . These points form an equilateral triangle .
As the triangle is equilateral so the lengths of the three sides of the triangle would all be the same so, .
Step 2. Find the distance and
The distance between the points and is given as:
The distance between the points and is given as:
Step 3. Form and solve the equation
The distance and would be the same, so:
Now square both sides of the equation and solve for .
So, the values of satisfying the condition are .
Hence, the correct option is B.