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anonymous
 one year ago
In a line segment AB point C is called a midpoint of line segment AB. Prove that every line segment has one and only one midpoint.
anonymous
 one year ago
In a line segment AB point C is called a midpoint of line segment AB. Prove that every line segment has one and only one midpoint.

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Ehsan18
 one year ago
Best ResponseYou've already chosen the best response.0take c(0,0) on origin and take coordinates of point A(a,0) and of point B(a,0) By applying distance formula prove that AC = CB...and hence proved, if you want complete solution I can provide it to you.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have to prove it using Euclid's Axioms.

Pawanyadav
 one year ago
Best ResponseYou've already chosen the best response.0A line is represented by a linear equation. So when you solve this equation for midpoint you will also get a linear equation. And you know A linear equation has only one solution. So you will get only one value for midpoint.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0To prove, you need show 2 different midpoints are the same. Let \(A=(X_A,Y_A), B=(X_B,Y_B)\) Suppose C, C' both are midpoints of AB. Since C is midpoint of AB, the coordinate of C is \(C =(\dfrac{X_A+X_B}{2}, \dfrac{Y_A+Y_B}{2})\) Since C' is also midpoint of AB, the coordinate of C' is \(C'=(\dfrac{X_A+X_B}{2},\dfrac{Y_A+Y_B}{2})\) Hence C = C'\(\implies\) there is only 1 midpoint of the segment AB
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