(B) The formula for the centroid $(G)$ of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ is given by $G = \left( \frac{x_1 + x_2

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$\left( \frac{10}{3}, \frac{7}{3} \right)$

(B) The formula for the centroid $(G)$ of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ is given by $G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$.Given vertices are $(2, 1)$,$(5, 2)$,and $(3, 4)$.Calculating the $x$-coordinate: $x = \frac{2 + 5 + 3}{3} = \frac{10}{3}$.Calculating the $y$-coordinate: $y = \frac{1 + 2 + 4}{3} = \frac{7}{3}$.Thus,the centroid is $\left( \frac{10}{3}, \frac{7}{3} \right)$.

Class 11 Mathematics Straight Line Points related to triangle

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The centroid of a triangle,whose vertices are $(2, 1)$,$(5, 2)$,and $(3, 4)$,is

IIT 1964 All IIT

A
$\left( \frac{8}{3}, \frac{7}{3} \right)$
B
$\left( \frac{10}{3}, \frac{7}{3} \right)$
C
$\left( -\frac{10}{3}, \frac{7}{3} \right)$
D
$\left( \frac{10}{3}, -\frac{7}{3} \right)$

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If the orthocentre of the triangle,whose vertices are $(1,2), (2,3)$ and $(3,1)$ is $(\alpha, \beta)$,then the quadratic equation whose roots are $\alpha+4\beta$ and $4\alpha+\beta$ is:

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Show that the area of the triangle formed by the lines $y=m_{1}x+c_{1}$,$y=m_{2}x+c_{2}$ and $x=0$ is $\frac{(c_{1}-c_{2})^{2}}{2|m_{1}-m_{2}|}$.

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The centroid of a triangle,whose vertices are $(2, 1)$,$(5, 2)$,and $(3, 4)$,is

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If the orthocentre of the triangle,whose vertices are $(1,2), (2,3)$ and $(3,1)$ is $(\alpha, \beta)$,then the quadratic equation whose roots are $\alpha+4\beta$ and $4\alpha+\beta$ is:

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