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Is it true that the center of the triangle, whose vertices are $(0, 0), (3, 3)$ and $(0, 2 \sqrt{3})$ is (0,0)?

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True

False

answer is B.

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Detailed Solution

We have been given the vertices

(0, 0), (3, 3)

and

(0, 2 \sqrt{3})

.
We know the center of the triangle is a centroid.
Let the

x_{1}, x_{2}, x_{3}, y_{1}, y_{2} and y_{3}

are coordinates of vertices of triangle, then the centroid of a triangle is,

x 1 + x 2 + x 3 3, y 1 + y 2 + y 3 3

Let the center of the triangle be O.
Substituting

x_{1} = 0, x_{2} = 3, x_{3} = 0, y_{1} = 0, y_{2} = \sqrt{3}, and y_{3} = 2 \sqrt{3}

, in the formula,

O = (\frac{0 + 3 + 0}{3}, \frac{0 + \sqrt{3} + 2 \sqrt{3}}{3})

O = 1, \sqrt{3}

Therefore, our statement is false.
The value of center of the triangle is

1, \sqrt{3}

Hence, option 2 is correct.

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