Question

The courtyard of an apartment complex is represented by the vertices T(4, 1), U(30, 11), and V(17, 36). Each unit represents 1 meter. A bench is located at the centroid of the courtyard. Which ordered pair gives the coordinates of the centroid?

Answer 1

`(x,y) = (17,16)`

Explanation:

Given

`T(x_1,y_1) = (4, 1)`

`U(x_2,y_2) = (30, 11)`

`V(x_3,y_3) = (17, 36)`

Required

Determine the coordinates of the centroid

The coordinate is calculated as:

`(x,y) = ((1)/(3)(x_1+x_2+x_3),(1)/(3)(y_1+y_2+y_3))`

Substitute values for x's and y's

`(x,y) = ((1)/(3)(4+30+17),(1)/(3)(1+11+36))`

`(x,y) = ((1)/(3)(51),(1)/(3)(48))`

`(x,y) = ((51)/(3),(48)/(3))`

`(x,y) = (17,16)`

Hence, the coordinates of the centroid is (17,16)