Question

Find the coordinates of the centroid of the triangle whose vertices are A(5,3),B(6,1) and C(7,8)​

Answer 1

Given:

Vertices of triangle A(5,3);B(6,1) and C(7,8)

To Find :

Coordinates of the centroid

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Explanation:

Median is the point which is equidistant from all three vertices of the triangle.

formula for finding centroid of a triangle when vertices are given :

$\bold{\boxed{x = \frac{x_{1}+ x_{2} + x_{3}}{3}}}$

$\bold{\boxed{y = \frac{y_{1}+ y_{2} + y_{3}}{3}}}$

Here , $x_{1}=5$;$x_{2}=6$ and $x_{3}=7$

$y_{1}=3$;$y_{2}=1$ and $y_{3}=8$

Now ,finding centroid:

$\bold{x = \frac{5 + 6 + 7}{3} = \frac{18}{3} = 6}$

$\bold{y = \frac{3 + 1 + 8}{3} = \frac{12}{3} = 4}$

Therefore ,the coordinates of the Centroid of a triangle are (6,4)

Answer 2

Given:

Vertices of triangle A(5,3);B(6,1) and C(7,8)

To Find :

Coordinates of the centroid

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Median is the point which is equidistant from all three vertices of the triangle.

formula for finding centroid of a triangle when vertices are given :

$\bold{\boxed{x = \frac{x_{1}+ x_{2} + x_{3}}{3}}}$

$\bold{\boxed{y = \frac{y_{1}+ y_{2} + y_{3}}{3}}}$

Here , $x_{1}=5$;$x_{2}=6$ and $x_{3}=7$

$y_{1}=3$;$y_{2}=1$ and $y_{3}=8$

Now ,finding centroid:

$\bold{x = \frac{5 + 6 + 7}{3} = \frac{18}{3} = 6}$

$\bold{y = \frac{3 + 1 + 8}{3} = \frac{12}{3} = 4}$

Therefore ,the coordinates of the Centroid of a triangle are (6,4)