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anonymous

  • one year ago

In a line segment AB point C is called a mid-point of line segment AB. Prove that every line segment has one and only one midpoint.

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  1. Ehsan18
    • one year ago
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    take c(0,0) on origin and take co-ordinates 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.

  2. anonymous
    • one year ago
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    I have to prove it using Euclid's Axioms.

  3. Pawanyadav
    • one year ago
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    A 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.

  4. Loser66
    • one year ago
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    To 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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