How do you prove that [tex]AM = \frac{1}{2}AB[/tex] if M is the midpoint of line AB? Provide 7 steps.

because a midpoint mean middle so A----------M----------B
AM is 1/2 of AB as well as BM is 1/2 of AB
4------------5----------6 if 5 is the midpoint how much is between 4 and 5 and 5 and 6

Answered by 5632 | 2024-06-10

If M is the **midpoint **of the **line **AB, then it can be state that, AM=1/2AB
What is midpoint of a line?
Midpoint is a point which is at the **equal **distance from the **both **the points.
Formula for midpoint,
P(Xₐ, Yₐ) = [ (X₁+X₂)/2 , (Y₁+Y₂)/2 ]
Given that,
M is the midpoint of line AB
We have to prove, AM = 1/2AB
where M is a mid-point
**Distance **between points A and B is
AB = distance of point M from A + distance of point M from B
AB = AM + BM
According to definition of mid-point
Distance of M from both the points are equal,
AM = BM
AB = AM + AM
AB = 2AM
AM = 1/2AB
Hence Proved
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Answered by subhashreeVT | 2024-06-17

We proved that A M = 2 1 ​ A B based on the definition of the midpoint. Since M is the midpoint, it divides AB into two equal segments. Thus, using algebraic substitution and simplification leads us to the required conclusion.
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Answered by subhashreeVT | 2024-10-01