Question

In the adjoining figure, ABC is an equilateral triangle
whose vertex A has the
coordinates (0,√ 3). Find the
coordinates of B and C.



​

Answer 1

Answer:

The ordinates of both B & C are 0.

So, BC= (abscissa of B−abscissa of C)=(5−1)=4units=a

The side of equilateral ΔABC.

∴ Its height=

2

3

a=

2

3

×4=2

3

units.

Also, the mid point of BC=(

2

5+1

,

2

0+0

)=(3,0).

Now, ΔABC is equilateral and BC is on the x-axis.

So, the abscissa of A will be the mid point of BC.

The ordinate of A will be the height of ΔABC from the mid point of BC.

∴ The coordinates of A are (3,2 √3).