Explanation
To determine the nature of the triangle formed by points A(-2, 0), B(2, 0), and C(0, √12), let's calculate the distances between each pair of points.
Step 1: Calculate the distance AB
AB = √((2 - (-2))² + (0 - 0)²) = √(4²) = √16 = 4
Step 2: Calculate the distance AC
AC = √((0 - (-2))² + (√12 - 0)²) = √(2² + (√12)²) = √(4 + 12) = √16 = 4
Step 3: Calculate the distance BC
BC = √((0 - 2)² + (√12 - 0)²) = √((-2)² + (√12)²) = √(4 + 12) = √16 = 4
Step 4: Determine the nature of the triangle
Since AB = AC = BC = 4, the triangle is equilateral.