The value of x is 7 for the given collinear points a, b, and c as b is the mid-point of ac.
According to the given question.
a, b, and c are collinear points. Which means all points a, b, and c lie in a same plane.
b is lies between a and c.
Also,
ab = x, bc = x and ac = 24.
Since, b lies in between a and c, and it is given that ab = x and bc = x.
Which means b is the mid point of ac.
Therefore,
ab + bc = ac
Substitute the values of ab, bc and ac in the above equation.
⇒ x + x = 14
⇒ 2x = 14
⇒ c = 14/2
⇒ c = 7
Therefore, the value of x is 7.
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