Question

find the vertices of an eqilateral triangle with base lying on X axis with origin as its mid point and each side 8 units
step by step answer ..... ​

Answer 1

Let BC be the base of equilateral △ABC.

It is given that BC = 2a and mid-point of BC is at the
origin.

Therefore, coordinates of B and C are (0,a) and (0,−a) respectively.

As the triangle ABC is equilateral.

So, vertex A lies on x-axis.

Let its coordinates be (x,0).

Also,AB=BC=AC⇒AB=AC=AC=2a

Using Pythagoras theorem in ΔAOB, we get

AB
2
=OA
2
+OB
2


⇒(2a)
2
=OA
2
+a
2


⇒OA=±
3
​
a

So,coordinates A are (−
3