Question 3 ivThe points Ax1-y1-Bx2-y2 and Cx3-y3 are the vertices of - ABC- What are the coordinates of the centroid of the triangle ABC-

Coordinate of the centriod of the Δ ABC = ( Sum of abscissa of all vertices/3,Sum of ordinate of all vertices/3 ) = ( x_1+x_2+x_3/3,y_1+y_2+y_3/3 ) ...

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Standard X

Mathematics

Centroid Formula

Question 3 iv...

Question

Question 3 (iv)
The points $A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})$ are the vertices of $Δ$ ABC. What are the coordinates of the centroid of the triangle ABC?

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Solution

Coordinate of the centriod of the $Δ$ ABC
$= (\frac{S u m o f a b s c i s s a o f a l l v e r t i c e s}{3}, \frac{S u m o f o r d i n a t e o f a l l v e r t i c e s}{3}) = (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$

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Similar questions

Q. Question 7 (v)
Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC.
(e) If

A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})

are the vertices of triangle ABC, find the coordinates of the centroid of the triangle.

Q. Question 3 (i)
The points

A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})

are the vertices of

Δ

ABC.
The median from A meets BC at D. find the coordinates of the point D.

Find the centroid of the triangle with vertices A $(x_{1}, y_{1})$ , B $(x_{2}, y_{2})$ and C $(x_{3}, y_{3})$ .

Show that the coordinates of the centroid of the triangle with vertices $A (x_{1}, y_{1}, z_{1})$ , $B (x_{2}, y_{2}, z_{2})$ and $C (x_{3}, y_{3}, z_{3})$ is $(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3}, \frac{z_{1} + z_{2} + z_{3}}{3})$ .

Q. Question 3 (iii)
The points

A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})

are the vertices of

Δ

ABC.
Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ:QE = 2:1 and CR:RF = 2:1.

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Question 3 (iv) The points A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of Δ ABC. What are the coordinates of the centroid of the triangle ABC?

Coordinate of the centriod of the Δ ABC =(Sum of abscissa of all vertices3,Sum of ordinate of all vertices3)=(x1+x2+x33,y1+y2+y33)

Question 3 (iv)
The points $A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})$ are the vertices of $Δ$ ABC. What are the coordinates of the centroid of the triangle ABC?

Coordinate of the centriod of the $Δ$ ABC
$= (\frac{S u m o f a b s c i s s a o f a l l v e r t i c e s}{3}, \frac{S u m o f o r d i n a t e o f a l l v e r t i c e s}{3}) = (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$