Question

the coordinates of two consecutive vertices A and B of a regular hexagon ABCDEF are (1,0) and (2,0). find the equation of diagonal CE?

Answer 1

 ⇒y − 3√ = 23√ − 3√2−32 (x−1)⇒y − 3√ = 3√−3(x−1)⇒y − 3√ = 13√(1−x)⇒3√y − 3 = 1−x⇒x + 3√y = 4

Answer 2

The equation of the diagonal CE is x +√3 y = 4

Step-by-step explanation:

Given data

For a regular hexagon, two consecutive vertices A and B having vertices

A = ( 1, 0)

B = ( 2,0)

Find the equation of the diagonal CE

If AB = 1 unit

Then BC, CD, DE and EF is also equals to 1 unit

BC = CD = DE = EF = 1 unit

The equation of a line is (y-$y_1$) = m ( x- $x_1$)

Where m is the slope

Find the values of  $y_1$, $x_1$ from the hexagonal diagram using the coordinates A ( 1,0) and B ( 2,0)

C (2+1 cos 60°, 1 sin 60°) = c((5÷2), (√3÷2))

E (1, 2 sin 60°) =E (1, √3)

Thus $x_1$, $y_1$ = ((5÷2), (√3÷2))

and $x_2$, $y_2$ = (1, √3)

Find the slope of the equation by using the formula

m = ($y_2$ - $y_1$) ÷ ($x_2$ - $x_1$) --------------> 1

Substitute the respective values in above equation

m = (√3 - (√3÷2)) ÷ ( 1- (5÷2))

m = (2√3 -√3) ÷ ( -3 )

m = -(1 ÷ √3)

Substitute the values of m , $x_2$ and $y_2$ in equation of a line

y- √3 = (-1÷√3) ( x-1 )

√3 y - 3 = -x + 1

√3 y = -x + 1 + 3

√3 y -x = 4

x + √3 y = 4

The equation of the diagonal CE is x + √3 y = 4 for a regular hexagon having two consecutive vertices A and B with coordinates ( 1, 0) and ( 2, 0).

To learn more ...

1. https://brainly.in/question/1516357

2. https://brainly.in/question/10818675