# The Base Bc of an Equilateral Triangle Abc Lies on Y-axis. the Coordinates of Point C Are (0, -3). Origin is the Midpoint of Base , Find the Coordinates of Another Point D Such that Abcd is a Rhombus. - Mathematics

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.

#### Solution

Let (0, y)  be the coordinates of B. Then

 0= (-3+y)/2 ⇒ y=3

Thus, the coordinates of B are (0,3)

Here. AB = BC = AC  and by symmetry the coordinates of A lies on x-axis Let the coordinates of A be (x, 0). Then

AB= BC⇒AB^2 = BC^2

⇒ (x-0)^2 +(0-3)^2 = 6^2

⇒ x^2 = 36-9=27

⇒ x = +- 3 sqrt(3)

"If the coordinates of point A are "(3 sqrt(3),0)  ."then the coordinates of D are " (-3 sqrt(3), 0).

"If the coordinates of point A are "(-3 sqrt(3),0)  ."then the coordinates of D are " (-3 sqrt(3), 0).

"Hence the required coordinates are " A(3sqrt(3),0) , B(0,3) and  D (-3 sqrt(3),0) or

A (-3sqrt(3),0) , B(0,3) and D (3sqrt(3),0).

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 31