**Q) If (-5,3) coordinates and (5,3) are two vertices of an equilateral triangle, then find of the third vertex, given that origin lies inside the triangle. (Take √3 = 1.7)**

**Ans: **

Let the third vertex be (x, y)

Hence, 3 vertex of the triangle will be A (-5,3) B (5,3) C (x y)

AB = 10 = AC By squaring both sides, we get AC² = 100

(-5-x )² + (3-y)² = (5-x)² + (3-y)² ………….(i)

=> 20 x = 0 or x = 0

Now substituting the value x = 0 in equation (i), we get:

(3-y)² = 75 or (3-y) = ±5√3

⇒ y = 3- 5√3 = -5.5 (by √3 = 1.7)

**Therefore, the coordinates of the third vertex are (0, -5.5)**