What is the centroid of a triangle with corners at $(1, 4)$ $(1, 4 )$ , $(3, 5)$ $(3, 5 )$ , and $(5, 3)$ $(5,3 )$ ?

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Answer 1 · 2017-04-30T07:22:00

The centroid is $= (3, 4)$ $=(3,4)$

Let $A B C$ $ABC$ be the triangle

$A = (x_{1}, y_{1}) = (1, 4)$ $A=(x_1,y_1)=(1,4)$

$B = (x_{2}, y_{2}) = (3, 5)$ $B=(x_2,y_2)=(3,5)$

$C = (x_{3}, y_{3}) = (5, 3)$ $C=(x_3,y_3)=(5,3)$

The centroid of triangle $A B C$ $ABC$ is

$= (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$ $=((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)$

$= (\frac{1 + 3 + 5}{3}, \frac{4 + 5 + 3}{3})$ $=((1+3+5)/3,(4+5+3)/3)$

$= (\frac{9}{3}, \frac{12}{3})$ $=(9/3,12/3)$

$= (3, 4)$ $=(3,4)$

What is the centroid of a triangle with corners at (1,4)(1, 4 ), (3,5)(3, 5 ), and (5,3)(5,3 )?