Question

If (0, - 3) and (0, 3) are the two vertices of an equilateral triangle, find the coordinates of its third vertex.

Answer 1

Answer:

Third vertex is (3,0).

Answer 2

Given :

(0, - 3) and (0, 3) are the two vertices of an equilateral triangle.

To find:

coordinates of its third vertex.

Solution:

Let the third  vertex of the equilateral ΔABC be A (x,y)

By distance formula,

d = √(x₂-x₁)² + (y₂-y₁)²

∴BC = √(0-0)² + (3+3)² = √6² = √36 = 6

∴AB = √(x-0)² + (y+3)²

=> AB² = x² + y² + 2y = 27 .....(1)

Now, AC = √(x-0)² +   (y-3)²  

=> AC² = x² + y² + 9 - 6y = 36

=> 27 -2y-6y+9 =36

=> -8y = 36 -36

=> y = 0

y = 0 in (1) gives x² = 27

Therefore, the required points are A (3√3,0) and A (-3√3,0)