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Step-by-step explanation:

As per picture we have:

Since GI = GJ + JI, substitute:

Then the lengths are:

As point J divides the segment IG in the ratio of 2:1 we can state it is the centroid of ΔFHI

see explanation

Step-by-step explanation:

From the diagram

GI = GJ + JI , substitute values

9x - 9 = 2x + 3 + 5x

9x - 9 = 7x + 3 ( subtract 7x from both sides )

2x - 9 = 3 ( add 9 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Thus

GJ = 2x + 3 = 2(6) + 3 = 12 + 3 = 15

JI = 5x = 5(6) = 30

GI = 9x - 9 = 9(6) - 9 = 54 - 9 = 45

The centroid is where the 3 medians of a triangle intersect.

On each median, the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.

Here JI = 30 and twice as long as GJ, thus J is the centroid of the triangle.

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step-by-step explanation: