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Standard XI

Mathematics

Centroid of a Triangle

In an equilat...

Question

In an equilateral $△ A B C$ coordinates of the centroid of the triangle is ( $1, 2, 3)$ . Find the coordinates of the orthocenter of the triangle.

$(1, 2, 3)$

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$(\frac{1}{2}, 1, \frac{3}{2})$

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$(1, 2, \infty)$

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$(0, 2, 3)$

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Solution

The correct option is A
$(1, 2, 3)$

It is given that $△ A B C$ is an equilateral triangle.

For an equilateral triangle coordinates of centroid, Incenter, orthocenter and circumcenter is same.

Coordinate of orthocenter is same as coordinate of centroid that is $(1, 2, 3)$

Option A is correct

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Similar questions

In a triangle coordinates of orthocenter and circumcenter are $(- 3, 5, 2)$ and $(6, 2, 5)$ . Find the coordinates of centroid of the triangle.

If a triangle has its orthocenter at (1, 1) and circumcenter at $(\frac{3}{2}, \frac{3}{4})$ , then the coordinates of the centroid of the triangle are

A B C

is an equilateral triangle. If the coordinates of two of its vertices are (

1, 3)

and

(- 2, 7)

the coordinates of the third vertex can be

Which of the following statements are correct?

1. For triangle orthocenter,circumcenter and

centroid are collinear.

2. Centroid divides the line joining the circumcenter $&$ orthocenter

in the ratio of $2 : 1$ i.e., $\frac{C S}{O C} = \frac{2}{1}$

Where C-Coordinate of centroid

O-Coordinate of orthocenter

S--Coordinate of circumcenter

Q. Assertion :Vertices of a triangle are

A (a, b), B (a + 1, b - 2), C (a - 2, b + 1)

. If the origin is shifted to the centroid of the triangle without rotation of axes, coordinates of

A

in the new system of coordinates are

(\frac{1}{3}, \frac{1}{3})

Reason: Centroid of an equilateral triangle is equidistant from its vertices

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In an equilateral △ABC coordinates of the centroid of the triangle is (1, 2, 3). Find the coordinates of the orthocenter of the triangle.

The correct option is A (1,2,3) It is given that △ABC is an equilateral triangle. For an equilateral triangle coordinates of centroid, Incenter, orthocenter and circumcenter is same. Coordinate of orthocenter is same as coordinate of centroid that is (1, 2, 3) Option A is correct

In an equilateral $△ A B C$ coordinates of the centroid of the triangle is ( $1, 2, 3)$ . Find the coordinates of the orthocenter of the triangle.

The correct option is A
$(1, 2, 3)$

It is given that $△ A B C$ is an equilateral triangle.

For an equilateral triangle coordinates of centroid, Incenter, orthocenter and circumcenter is same.

Coordinate of orthocenter is same as coordinate of centroid that is $(1, 2, 3)$

Option A is correct