Question

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 point A and B ,also find the coordinates of point D such that BACD is a rhombus

Answer 1

Answer:

Step-by-step explanation:

since origin (0,0) is the mid point of base BC

let coordinates of point B(x1,y1)

C(0,-3)

0=(x1+0)/2 and     0=(y1 -3)/2

x1=0  and y1=3

B(0,3)

length of base BC=6

point A will lie on x axis

AB=6 (equilateral triangle)

OA=sqrt(AB^2 - BO^2)   by pythogorous theorem

OA=sqrt(36 - 9)

OA=3sqrt3

cordinates of point A=(3,0)

                              and(-3,0)

D=(-3,0)

and (3,0)

Answer 2

Answer:

given ,

coordinate of c=(0,-3)

and origin is the  midpoint

here,

if origin is the midpoint then the either side of the axis should be the additive inverse of one another,

so coodinate of b = (0,3)

now length of bc = 6 units

so, ab = bc = ac = 6units

now,

ao=3√3

so coodinate of a = (3√3 , 0)