Question

the base BC of an equilateral triangle abc lies on y axis the coordinates of point C is (0,-3 ) . the origin is the mid point of base. find the coordinates of A and B . also find the coordinates of another point D such that ABCD is a rhombus. 8​

Answer 1

Answer:

ANSWER

O is the mid-point of the base BC.

Therefore, coordinates of point B are (0,3).

So, BC = 6 units

Let the coordinates of point A be (x,0).

Using distance formula,

AB=

(0−x)

2

+(3−0)

2

=

x

2

+9

BC=

(0−0)

2

+(−3−3)

2

=

36

Also, AB = BC

x

2

+9

=

36

x

2

+9=36

x

2

=27

x=±3

3

Coordinates of A = (3

3

,0).