The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, –3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another point D such that ABCD is a rhombus.
Given: The base (BC) of the triangle lies on y -axis, where, B has the coordinates: (0, -3).
Now, Δ ABC is in equilateral triangle
∴ AB = AC = BC …(1)
The figure is shown below:
BC = √(0)2 + (-3-3)2
⇒ BC = √62
⇒ BC = 6 units.
Now, AC = 6 units
⇒ √x2+(-3)2 = 6 units
⇒ x2 + 9 = 36
⇒ x2 = 25
⇒ x = +5
∴ The coordinate of the point A are (5, 0)
Similarly, if ABCD is a rhombus, then AB = BD = DC= CA
Hence, we can say that the coordinate of the point D are (-5,0)
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