Question

C bisects AB. If AC = 8x - 1 and BC = 4x + 19, what is the length of AB?

Answer 1

The length of AB is 78 units.

What is a Line Segment?

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure is given below shows a line segment AB , where the length of line segment AB refers to the distance between its endpoints, A and B.

Given that C is the midpoint of AB

AC = 8x - 1 and BC = 4x + 19,

A______________C______________B

⇒ AB = AC+ BC

Since C is the bisects of AB, So AC = BC

⇒ AB = AC+ BC

⇒ AB = 2AC

Substitute the values of If AC = 8x - 1 and BC = 4x + 19,

⇒ 8x - 1 = 4x + 19,

Rearranging the terms in the above equation,

⇒ 8x - 4x  = 1 + 19,

⇒ 4x = 20,

⇒ x = 20/4,

⇒ x = 5

So AB = 2AC

⇒ AB = 2(8x - 1) = 16x -2

Substitute the value of x = 5 in the above equation,

⇒ AB = 16(5) -2

⇒ AB = 78

Hence, the length of AB is 78 units.

Learn more about the line segment here:

brainly.com/question/25727583

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