Question

Point G bisects the line segment FH. The length of FG is 16 less than 3 times the length of GH. What is the length of FH?

Answer 1

Answer: FH = 16

PART I

Concept:

Bisect means to cut or divide something into two equal parts.

In mathematics, usually bisect means cutting a segment or an angle.

If you are still confused, you may refer to the attachment below for a graphical explanation or tell me.

Solve:

Given information

FG is 16 less than 3 times the length of GH

Let x be the length of GH

Given expression

FG = GH

Set equation

3x - 16 = x

Add 16 on both sides

3x - 16 + 16 = x + 16

3x = x + 16

Subtract x on both sides

3x - x = x + 16 - x

2x = 16

Divide 2 on both sides

2x / 2 = 16 / 2

x=8

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PART II

Concept:

In order to find the length of FH, we need to know the idea of the segment addition postulate.

The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

Solve:

Given information

FG = GH = x

x = 8

Given expression deducted from the segment addition postulate

FH = FG + GH

Substitute values into the expression

FH = x + x

FH = 8 + 8

$\boxed {FH=16}$

Hope this helps!! :)

Please let me know if you have any questions