Question

If two vertices of an equilateral triangle are (3,0) and (6,0), find the third vertex



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Answer 1

it is a right solution

Step-by-step explanation:

I hope it help

Answer 2

Answer:

Concept:

Since,it is a equilateral triangle hence the distance between the sides is same.

And the distance of the points are same so y ordinate is 0

Coordinate=(x,0)

Hence,distance formula

$\sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$

Location of points would be:

(x,0)

(3,0) (6,0)

Applying the formula:

$\sqrt{ {(x - 3)}^{2} + ( {0 - 0)}^{2} }$

$\sqrt{ {(x - 3)}^{2} + ( {0 - 0)}^{2} } = \sqrt{ {(x - 6)}^{2} - ( {0 - 0)}^{2} }$

Since,0-0 is 0 only so we remove zero

$\sqrt{ {(x - 3)}^{2} } = \sqrt{( {x - 6)}^{2} }$

$\sqrt{ {x}^{2 } - 6x + 9} = \sqrt{ {x}^{2} - 12x + 36 }$

Squaring both the sides:

${x}^{2} - 6x + 9 = {x}^{2} - 12x + 36$

${x}^{2} \: \: got \: \: cancelled$

$- 6x + 9 = - 12x + 36$

$- 6x + 12x = 36 - 9$

$6x = 27$

$x = \frac{27}{6}$

$x = \frac{9}{2} = 4.5$

Coordinate=(4.5,0)

Verification:

(4.5-3)^2=(6-4.5)^2

1.5^2=1.5^2

2.25=2.25

Since,LHS=RHS

Hence,

The given solution:

Third vertex=(4.5,0)