Answer: AB = 9
Step-by-step explanation:
Since B is the midpoint, AB and BC must be congruent (since theyre both half of the segment). The equation is:
2x + 5 = 5x - 1
This means x = 2, meaning AB is 9.
The length of line AB is 9 units.
The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment.
According to the given question.
Point b is the midpoint of a and c.
Therefore,
AB = BC..(i)
Also, it is given that
AB = 2x + 5 and BC = 5x -1
So, from (i)
[tex]2x+5 = 5x -1[/tex]
⇒[tex]5+1=5x -2x[/tex]
⇒[tex]6 = 3x[/tex]
⇒[tex]x = 2[/tex]
Thus, the length of AB is given by
[tex]AB= 2(2)+5 = 9unit[/tex]
Hence, the length of line AB is 9 units.
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