Question

What will be the Centroid of the triangle whose vertices are x(-2,4),y(5,2)&z(4,3).​

Answer 1

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

$\sf \: Coordinates \: of \: the \: vertices \: are: \: x(-2,4), \: y(5,2) \: and \: z(4,3)$

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

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

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

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

$\sf \: x(-2,4) \: \rightarrow \: (x_{1}, y_{1}) \\ \\\sf \: y(5,2) \: \rightarrow \: (x_{2}, y_{2}) \\ \\ \sf \: z(4,3) \: \rightarrow \: (x_{3}, y_{3})$

$\large{\pink{\bold{\underline{Now:}}}} \\ \\ \rightarrow \: \sf \: Centroid = ( \frac{-2 + 5 + 4}{3}) ,( \frac{4 + 2 + 3}{3} ) \\ \\ \rightarrow \sf \: Centroid = ( \frac{-2 + 9}{3}) , (\frac{9}{3} ) \\ \\ \rightarrow \sf \: Centroid = ( \frac{7}{3} ),( \frac{\cancel9}{\cancel3} ) \\ \\ \rightarrow \sf \: Centroid = (2.3,3)$

$\large{\orange{\bold{\underline{Therefore:}}}} \\ \\ \sf \: The \: coordinates \: of \: Centroid \: of \: the \: triangle \\ \sf \: is \: (2.3,3).$

Answer 2

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

Coordinates of the vertices are: x(-2,4),y(5,2) and z(4,3)

$\large { \bold { \pink { \underline {To \: find:}}}}$

Centroid of the triangle

$\large { \bold { \purple { \underline {Solution: }}}}$

x (-2,4) arrow (x1, y1)

y (5,2) arrow (x2,y2)

z (4,3) arrow (x3,y3)

$\large { \bold { \orange { \underline {Now: }}}}$

Arrow cendtroic ≈ $( \frac{ - 2 + 5 + 4}{3} )</em><em>,</em><em> ( \frac{4 + 2 + 3}{3} )$

Arrow cendtroic ≈ $( \frac{7}{3})</em><em>,</em><em> </em><em>( \frac{9}{3} )$

Arrow centroid ≈ (2.3,3)

$\huge \large \underline{ \blue{hope \: it \: help \: you}}$