Question

HELP 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.

Answer 1

D is the answer my friend C:

Answer 2

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
`(AD)/(AE) =(12)/(12+4)=(12)/(16) =(3)/(4)\\eq (2)/(3) ,` 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
`(AD)/(DE) =(12)/(4)=(12)/(16) =(3)/(1)\\eq (2)/(1),` option D is true.

Answer: correct choice is D.