A triangle has corners at $(7, 9)$ $(7 ,9 )$ , $(1, 7)$ $(1 ,7 )$ , and $(6, 8)$ $(6 ,8 )$ . How far is the triangle's centroid from the origin?

Question

A triangle has corners at $(7, 9)$ $(7 ,9 )$ , $(1, 7)$ $(1 ,7 )$ , and $(6, 8)$ $(6 ,8 )$ . How far is the triangle's centroid from the origin?

1 Answer

Impact of this question

1390 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-16T08:36:46

The distance of triangle's centroid from the origin is $9.262$ $9.262$ units

Explanation:

The centroid of a triangle whose vertices are $(x_{1}, y_{1})$ $(x_1,y_1)$ , (x_2,y_2) $and (x_{3}, y_{3})$ $and (x_3,y_3)$ is given by

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

Hence centrid of given triangle is $(\frac{7 + 1 + 6}{3}, \frac{9 + 7 + 8}{3})$ $((7+1+6)/3,(9+7+8)/3)$ or $(\frac{14}{3}, 8)$ $(14/3,8)$

and its distance from origin is

$\sqrt{{(\frac{14}{3})}^{2} + 8^{2}} = \sqrt{\frac{196}{9} + 64} = \sqrt{\frac{772}{9}} = \frac{1}{3} \times 27.785 = 9.262$ $sqrt((14/3)^2+8^2)=sqrt(196/9+64)=sqrt(772/9)=1/3xx27.785=9.262$

Science

Math

Humanities

... and beyond

A triangle has corners at $(7, 9)$ $(7 ,9 )$ , $(1, 7)$ $(1 ,7 )$ , and $(6, 8)$ $(6 ,8 )$ . How far is the triangle's centroid from the origin?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A triangle has corners at (7,9)(7 ,9 ), (1,7)(1 ,7 ), and (6,8)(6 ,8 ). How far is the triangle's centroid from the origin?

1 Answer

Explanation:

Related questions

Impact of this question

A triangle has corners at $(7, 9)$ $(7 ,9 )$ , $(1, 7)$ $(1 ,7 )$ , and $(6, 8)$ $(6 ,8 )$ . How far is the triangle's centroid from the origin?