Pls with 10th grade geomtry
based on the diagram, can point d be the centroid of triangle acf? explain.
yes, point d is the point of intersection of segments drawn from all three vertices.
yes, de is three-quarters of the length of the full segment.
no, de should be longer than ad.
no, the ratio between ad and de is 3: 1.

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point D which is also the intersection of three triangle's medians.

The centroid theorem states that the centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side.

Since you can state that D is not centroid (options A and B are not true).

By the centroid theorem, DE should be half of AD (AD should be twice longer), then option C is false.

Since option D is true.

correct choice is D.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2