Question

Each figure shows a triangle with one or more medians.


Find x if FY = x and YS = 2x-6 Find x if FS = x and FY = x


I am having trouble figuring this out so help will be greatly appreciated!

Answer 1

Applying the centroid theorem, the value of x in the given triangle in the figure is: B. 4

What is the Centroid Theorem?

The point where the three median of a triangle meet is the centroid. According to the centroid theorem, the centroid is 2/3 of the distance from each midpoint of the opposite sides to each vertex of the triangle.

Based on the centroid theorem, we have:

FY = 2/3(FS)

Substitute

x = 2/3(x + 2x - 6)

x = 2/3(3x - 6)

3x = 2(3x - 6)

3x = 6x - 12

3x - 6x = -12

-3x = -12

x = -12/-3

x = 4 (option B)

Learn more about the centroid theorem on:

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