Question

find the coordinates of A of an equilateral triangle ABC whose coordinates of B and C are -5, 0 and 5,0​

Answer 1

Answer:

(0, 2.5√6)

Step-by-step explanation:

Using distance formula, BC = √5² + 5² = 5√2

Mid point of BC = (-5+5/2 , 0+0/2)

                          = (0 , 0)

Area of triangle = √(3)/4 a²

1/2  * base * height = √(3)/4 a²

1/2 * a * height = √(3)/4 * a * a

height = √(3)/2  * a = √(3)/2 * (5√2)

          =  2.5√6

 As Mid point is at origin, height will be on the same line, means, its x-coordinate is 0, and height is 5√(3/2).

Hence the (0, 2.5√6) or (0, 5√(6)/2 ).