Question

The base BC of an equilateral triangle ABC is on y axis. The co-
ordinates of the point Care (0, -3). The origin is the midpoint of the
base. Find the co-ordinates of the points A & B .Also find the co-
ordinates of another point D such that BACD is a rhombus
Please give answer with steps I will mark brainliest,

Answer 1

Given ΔABC is an equilateral triangle (so, all the sides are equal)

Also given, O (origin) is the midpoint of the base BC.

C (0,-3)

So, B (0,3) and BC is 6 units.

Let A be (x,0)

Distance formula = √(x2 – x1)² + (y2 – y1)²

AB = √(0-x)²+(3-0)²

     = √x²+9 units

BC = √(0-0)²+(-3-3)²

     = √6²

     = √36

     = 6 units

We know that AB = AC (sides of an equilateral triangle)

So, equating AB and AC

√x²+9 = √36

x² + 9 = 36

x² = 36 - 9

x² = 27

x = √27

(Simplifying √27)

x = ±3√3

Since, A lies on X axis, it is a positive value

So, A (3√3,0)

Considering rhombus BACD, point D lies on the X' axis (where the values are negative)

So, D (-3√3,0)

Therefore, A (3√3,0); B (0,3); C (0,-3) and D (-3√3,0)