The length of AB is 78 units.
<h3>What is a Line Segment?</h3>
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:
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and get a common denominator of 8 on the right:
. Now simplify and cross-multiply: 39x = -16 andx = -16/39