Question

In figure given above triangle ABC is an equilateral triangle with co-ordinates of B and C as B (1,0) and C (5,0) Find the coordinates of vertex A.

Answer 1

Given,

ABC is  an  equilateral triangle,Clearly,

BC = 5 - 1 = 4 units

AB = BC = AC = 4 units.

Draw  a perpendicular on BC as  show in figure it wiil intersect  BC at  point (3,0) as  we know that  perpendicular  intersect  at  mid  point  of  equilateral triangle.

Now,

In triangle ABD,

AB²=  AD² +  BD²

4² =  AD² + 2²

16 - 4 = AD²

AD² = 12

AD = 2√3 units.

Hence,

Coordinates  of  A = (3, 2√3)