The base BC of an equilateral ABC lies on y- axis.The coordinates of point C are (0, -3).If the origin is the mid- point of the base BC, find the coordinate
Coordinate point of C is (0,-3)
Let the other point of base be B(0,p)
It is given that Origin O(0,0) is the mid point of B(0,p) and C(0,-3)
Using section formula we get,
0 = (p+(-3))/2
p = 3
Hence (0,3) is coordinate point B.
It is given that ABC is an equilateral triangle.
So, AB = BC = AC
Let the coordinate of the other vertice be (x,y)
Now using diatnace formula AB = BC = AC
x2 + (y-3)2 = 6 = x2 + (y+3)2
On equating we get y = 0 and x =3 3
Hence the coordinate point of B and A are (0,3) and (33, 0) respectively.