Question

The base BC of an equilateral triangle ABC lies on
y-axis. The co-ordinates of point Care (0,3). The
origin is the mid-point of the base. Find the co-
ordinates of the point A and B. Also find the co-
ordinates of another point D such that BACD is a
rhombus.​

Answer 1

Answer:

let the coordinates of B are (x,y)..

using mid point theorem

y+3/2 = 0

y= -3

x+0/2=0

x=0

coordinates of B are (0, -3)

...

all 3 sides are equal..

BC^2 = {(-3-3)^2+(0_0)^2}

BC = 6 units ..

using Pythagoras theorem

AO^2 = AB^2 - OB^2

AO = 3(3^1/2)

Coordinates of A = (-3(3^1/2) , 0)