Question

In figure , ABC and ABD are equilateral triangles . find the coordinate of points C and D.

Answer 1

chk solution..........

Answer 2

Answer:

C = (0, a√3)

and,

D = (0, -a√3)

Step-by-step explanation:

In the figure,

ABC and ABD are two equilateral triangles.

The length of side AB = 2a

Now,

Length of the side BC should be = AB = 2a

So,

Let us say the co-ordinate of the point C is (0, y).

So,

Length of side BC is given by,

$AB=BC=\sqrt{(a-0)^{2}+(0-y)^{2}}\\2a=\sqrt{a^{2}+y^{2}}\\4a^{2}=a^{2}+y^{2}\\y^{2}=3a^{2}\\y=a\sqrt{3}$

Therefore, the co-ordinate of the point C will be,

C = (0, a√3)

Also,

The co-ordinate of the point D will be just opposite of the co-ordinate of the point C, that is,

D = (0, -a√3)

Therefore, the co-ordinate of the points C and D are (0, a√3) and (0, -a√3).