Question

In angleABC, G is the centroid and GE=4. Find AG.

Answer 1

To find AG in angle ABC with G as the centroid and GE=4, we can use the properties of a centroid. AG is divided into two segments: GG' and G'M. Given that GG' = 4 and G'M is twice as long as GG', we can calculate AG by multiplying GG' by 3. So AG = 12.

Step-by-step explanation:

To find AG in angle ABC with G as the centroid and GE=4, we can use the properties of a centroid. The centroid divides the median (AG in this case) into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side. Therefore, AG is divided into two segments: GG' and G'M. Given that GG' = 4 and G'M, the value we need to find, is twice as long as GG', we can calculate AG by multiplying GG' by 3. So AG = 4 * 3 = 12.

Answer 2

keeping in mind that a centroid cuts all medians at a 2 : 1 ratio, meaning that the median AE gets cut on a 2 : 1 ratio, meaning AG : GE = 2 : 1, Check the picture below.