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
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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).
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