 Krishna
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Step 1: Recall the distance between two points formula

NOTE: Measure the distance between the points. to know the lengths

of the three sides of the triangle.

FORMULA: d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2\ }\ -\ y_1\right)^2}\

Step 2: Find the tree lengths of the equilateral triangle. Using the distance between the two points formula.

NOTE: In equilateral triangle  all sides are equal

EXAMPLE:  AC = \sqrt{(x - 0)^2 + (y - 0)^2} = 12

AC = \sqrt{x^2 + y^2} = 12 (given)

AC =   x^2 + y^2 = 12^2.................(1)

AB = \sqrt{b^2} = 12

b = 12..........................(2)

BC = \sqrt{(x - b)^2 + (y - 0)^2 } = 12

\sqrt{(x - b)^2 + (y)^2 } = 12 ................(3)

Step 3: Find the x value by simplifying the equations

NOTE: Solve the equations in step 2

EXAMPLE: Substitute the b value in the equation (3)

\sqrt{(x - 12)^2 + (y)^2}  = 12

(x)^2 - 2*12*x + (12)^2 + (y)^2 = (12)^2

x^2 + y^2 - 24x + (12)^2 = (12)^2

We can x^2 + y^2 = 12^2 since equation (1)

12^2 - 24x + 12^2 = 12^2

- 24x = 12^2

x = - \frac{144}{24}

x = - 6

Step 4: Substitute x value in the equation (1) to find the y value.

EXAMPLE: x^2 + y^2 = 12^2

(-6)^2 + y^2 = 12^2

36 + y^2 = 144

y^2 = 108

y = 6 \sqrt{3}

Coordinates of C = (-6, 6 \sqrt{3} )