Question

Calculate the Centroid of the triangle whose vertices are x(5,1),y( 7,1) and z(3,3).​

Answer 1

Answer:

ANSWER

given points A(4,3),B(3,4),C(2,2)

Circumcenter is given as (

3

4+3+2

,

2

3+4+2

)

(

3

9

,

3

9

)=(3,3)

Answer 2

$\large{\red{\bold{\underline{Given:}}}}$

$\sf \: Coordinates \: of \: the \: vertices \: are: \: x(5,1), \: y(7,1) \: and \: z(3,3)$

$\large{\green{\bold{\underline{To \: Find:}}}}$

$\sf \: Centroid \: of \: the \: triangle$

$\large{\blue{\bold{\underline{Formula \: Used:}}}} \\ \\ \sf \:Coordinates \: of \:Centroid = \: (\frac{x_{1} + x_{2} + x_{3}}{3} ),( \frac{y_{1} + y_{2} + y_{3}}{3})$

$\large{\red{\bold{\underline{Solution:}}}} \\ \\ \: \sf \: On \: considering \: the \: respective \: coordinates \: as :$

$\sf \: x(5,1) \: \rightarrow \: (x_{1}, y_{1}) \\ \\\sf \: y(7,1) \: \rightarrow \: (x_{2}, y_{2}) \\ \\ \sf \: z(3,3) \: \rightarrow \: (x_{3}, y_{3})$

$\large{\pink{\bold{\underline{Now:}}}} \\ \\ \rightarrow \: \sf \: Centroid = ( \frac{5 + 7 + 3}{3}) ,( \frac{1 + 1 + 3}{3} ) \\ \\ \rightarrow \sf \: Centroid = ( \frac{\cancel15}{\cancel3}) , (\frac{5 }{3} ) \\ \\ \rightarrow \sf \: Centroid = ( \frac{5}{1} ),( \frac{5}{3} ) \\ \\ \rightarrow \sf \: Centroid = (5,1.6)$

$\large{\orange{\bold{\underline{Therefore:}}}} \\ \\ \sf \: The \: coordinates \: of \: Centroid \: of \: the \: triangle \\ \sf \: is \: (5,1.6).$